Methods, apparatus and systems for managing energy assets

ABSTRACT

The apparatuses and methods herein facilitate generation of energy-related revenue for an energy customer of an electricity supplier, for a system that includes an energy storage asset. The apparatuses and methods herein can be used to generate operating schedules for a controller of the energy storage asset. When implemented, the generated operating schedules facilitates derivation of the energy-related revenue, over a time period T, associated with operation of the at least one energy storage asset according to the generated operating schedule. The energy-related revenue available to the energy customer over the time period T is based at least in part on a wholesale electricity market.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims priority to and benefit of United StatesProvisional Application No. 61/477,067, filed on Apr. 19, 2011, U.S.Provisional Application No. 61/552,982, filed on Oct. 28, 2011, and U.S.Provisional Application No. 61/554,390, filed on Nov. 1, 2011. Thisapplication also claims priority to and benefit of U.S. Non-provisionalapplication Ser. No. 12/850,918, filed on Aug. 5, 2010, which claimspriority to U.S. Provisional Application No. 61/279,589, filed on Oct.23, 2009. The entire disclosure of these applications is incorporatedherein by reference in its entirety, including drawings.

BACKGROUND

In various regions across the United States, “regional transmissionoperators” (RTOs) or “independent system operators” (ISOs) generally areresponsible for obtaining electricity from electricity generators (e.g.,operators of coal-fired plants, gas plants, nuclear plants,hydroelectric plants, renewable resources, etc.), and then transmittingthe electricity provided by generators over particular geographicregions (e.g., New England, the greater New York area, the mid-Atlanticstates) via an electricity transmission infrastructure (also commonlyreferred to as the electricity “grid”). RTOs/ISOs also are responsiblefor maintenance of the grid, and RTOs generally are responsible forregional planning of grid expansion and/or deployment of new electricitytransmission infrastructure.

The Federal Energy Regulation Commission (FERC) presently requires that,in addition to generally managing the operation of the electricity gridin a given geographic area, RTOs/ISOs need to manage the price ofelectricity generated and consumed on the grid via “wholesaleelectricity markets.” To this end, RTOs/ISOs establish pricing auctionsto provide and support wholesale electricity markets. These pricingauctions, in addition to setting wholesale prices as a function of time,also foster sufficient electricity production for the grid at variouslocations to ensure that the grid is capable of delivering adequateelectricity to respective locations of demand for electricity on thegrid. Thus, some of the key objectives of the RTOs/ISOs in overseeingwholesale electricity markets include providing for efficient, economicand reliable operation of the grid.

In general, a given RTO/ISO supports a wholesale electricity market byallowing competing electricity generators to offer their electricityproduction output to the RTO/ISO. Retail electricity suppliers, alsocommonly referred to as “utilities,” in turn supply electricity toend-users/consumers, or “energy customers” of the retail electricitysuppliers, and are billed by the RTO/ISO for their purchases. Withrespect to the wholesale electricity market, the retail electricitysuppliers make bids for the electricity production output offered by theelectricity generators that, once accepted, establish market prices. Theretail electricity suppliers in turn typically re-price the electricitythey purchase from electricity generators on the wholesale market tosell to their retail electricity customers.

One significant issue facing RTOs/ISOs relates to various limitationsthat exist in connection with the grid that may impede a sufficient flowof electricity on the grid under certain circumstances. In particular,there may be time-dependent and/or geographically-dependent limitationson the grid's ability to support transmission of electricity, based onone or more of: 1) an available overall supply of electricity fromelectricity generators; 2) overall demand from retail electricitysuppliers; 3) general conditions on the grid itself (e.g., aging,failing or dated equipment); and 4) “location-specific” or “congestion”issues, e.g., respective geographic locations on the grid of electricitygenerators, electricity consumers, particular demand conditions, and/orparticular grid-related conditions that in some manner impede thetransmission of available electricity to one or more portions of thegrid). In some circumstances, a grid limitation may be caused by aparticular branch of the grid reaching a thermal limit, or a failure ofa generator or transformer on a branch of the grid; these limitationsgenerally are referred to as “security constraints” (i.e., particulargrid infrastructure cannot be overloaded without jeopardizing the grid).As such, the electricity grid is sometimes referred to as a “securityconstrained system.”

In view of the foregoing, RTOs/ISOs may employ a process known as“security constrained economic dispatch” for establishing wholesaleelectricity prices on a wholesale electricity market. Pursuant to thisprocess, an RTO/ISO managing a particular geographic region of anelectricity grid determines particular locations on the grid, or“nodes,” at which there is a possibility for security constraints tolimit electricity transmission. Wholesale electricity prices as afunction of time are then established independently for each node (i.e.,on a geographically-dependent, or “locational” basis) by accepting bidsfrom energy generators in sequence from the lowest priced offer to thehighest priced offer, up to an amount of electricity needed to satisfyelectricity demand conditions (e.g., bids from retail electricitysuppliers) at the node, so as to develop a supply and demand equilibriumprice. In this manner, the wholesale electricity price at a particularnode reflects the highest-priced accepted generation offer needed toprovide an adequate amount of electricity to that node, taking intoconsideration various security constraints that may be present at thenode. This location-based approach to wholesale electricity prices,which takes into consideration security constraints on the grid,commonly is referred to as “locational marginal pricing,” and thewholesale electricity price at a given node is commonly referred to aLocational Marginal Price (LMP). Thus, the wholesale electricity pricegenerally varies at different locations on the grid, based at least inpart on security constraints.

While electricity generators and retail electricity suppliers make up asignificant constituency of the participants in wholesale electricitymarkets, applicable market rules in some wholesale electricity marketsalso permit electricity consumers/end-users (e.g., energy customers ofretail electricity suppliers) and others to participate in wholesaleelectricity markets so as to earn energy-related revenue and offsettheir energy-related expenditures. In particular, market rules nowpermit energy users (or their market representatives) to make offers tocurtail or otherwise alter their electricity use, or to sellself-generated or stored electricity, to the wholesale market. If suchan offer by an energy customer to provide an “electricity-relatedproduct or service” is accepted on the applicable wholesale market, thecustomer endeavors to appropriately control its various energy assets soas to make available to the grid the offered product/service, in returnfor payment pursuant to the terms of the offer. The concept of an energycustomer providing an electricity-related product or service (e.g.,electricity use curtailment) on a wholesale electricity market inexchange for payment to the energy customer by the RTO/ISO, commonly isreferred to as “demand response” (DR).

Some of the currently more active wholesale electricity sub-markets inwhich energy customers of retail service providers may readilyparticipate include the “energy markets” (e.g., “day-ahead” energymarket, “real-time dispatched” energy market). While various pricingmodels exist for participation in these markets and other economicdemand response wholesale electricity markets (as well as variouspenalty models for customer non-performance pursuant to an offer toreduce/curtail energy use), often any revenue generated by the energycustomer from participation in these markets is based on the locationalmarginal price (LMP). The LMP may be calculated periodically atspecified nodes (e.g., every 5 minutes, every half-hour, every hour)depending on the particular market in which the energy customer isparticipating. More generally, revenue generation relating toparticipation in an economic demand response wholesale electricitymarket is based on a prevailing “wholesale electricity price” for theparticular market in question, which in turn generally is based on theLMP (calculated at various intervals), as discussed above.

To determine revenue earned by participating energy customers in aparticular economic demand response wholesale electricity market such asan “energy market,” the amount of electricity use reduction by theparticipating customer typically has to be measured; subsequently, thismeasured amount of electricity use reduction typically is multiplied bya price relating to the prevailing wholesale electricity price for themarket in question (e.g., LMP). Electricity use reduction by the energycustomer conventionally is measured against a reference electricityusage commonly referred to as a “customer baseline” (CBL). The CBL isintended to represent what the participating energy customer'selectricity use normally would have been, over a particular time periodand typical (“business-as-usual” or BAU) operating conditions for thecustomer's energy assets, absent the customer's voluntary electricityuse reduction based on the incentive provided by the economic demandresponse wholesale electricity market.

Conventionally, a customer baseline (CBL) electricity use profile for anenergy customer is derived by an RTO/ISO from an historical sample ofactual electricity use by the customer over a particular time period andBAU operating conditions. In some cases, the particular time period forwhich an historical sample of the customer's actual electricity use isselected as a CBL may be based, at least in part, on similar conditionsprevailing at the customer's site at the time of the historical samplingand participation in the economic demand response program (e.g., similarweather conditions, similar seasons/time of year, similar occupancyconditions at the customer's site, etc.). In other instances, the timeperiod for selecting an historical sample of actual electricity usage asa CBL is based on relatively recent actual electricity use by the energycustomer just prior to the customer's participation in the economicdemand response program. For example, the ISO PJM Interconnectcalculates a market-participating customer's CBL for a given weekday as“the average of the highest four out of the five most recent highestload (electricity use) weekdays in the 45 calendar day period precedingthe relevant load reduction event.” In sum, revenue generation from theeconomic demand response wholesale electricity “energy markets”conventionally is based on an historical actual electricity usage of aparticipating customer, which historical actual electricity usage servesas a customer baseline (CBL) against which electricity use reduction ismeasured for purposes of paying the energy customer for the usereduction.

SUMMARY

The Inventors have recognized and appreciated that new opportunities forparticipation in wholesale electricity markets by electricityconsumers/end-users (e.g., energy customers of retail electricitysuppliers) have created a need for energy management tools to facilitateenergy-related revenue generation from such markets. In view of theforegoing, various embodiments are directed generally to methods,apparatus and systems for determining operating schedules for energyassets so as to facilitate revenue generation from wholesale electricitymarkets. These energy assets include energy storage assets, energyconsuming assets and energy generating assets.

Wholesale electricity markets in which the energy customer mayparticipate to earn energy-related revenue, and to which the variousmethods, apparatus and systems according to the concepts disclosedherein may apply, include various economic demand response wholesaleelectricity markets, examples of which include, but are not limited to,a “real-time energy market,” a “day-ahead energy market,” a “day-aheadscheduling reserve market,” a “synchronized reserve” market, a“regulation” market, a “capacity” market, and an “emissions” market. Insome examples, the inventive methods, apparatus and systems describedherein may be implemented in whole or in part by a curtailment serviceprovider (CSP) or other entity acting as a “broker” between energycustomers and an RTO/ISO to facilitate participation in various demandresponse programs supported by wholesale electricity markets.

Suggested Operating Schedules for Energy Assets

In exemplary implementations discussed in greater detail below, theinventive methods, apparatus and systems described herein determine asuggested operating schedule for one or more energy assets (includingenergy-consuming assets for which energy usage may be curtailed), over agiven time period T, that are operated by an energy customer of a retailelectricity supplier. The energy assets operated by the energy customermay include electricity-consuming assets as well aselectricity-generating assets (e.g., fossil-fuel-based generators,renewable energy sources) and/or electricity storage assets (e.g.,batteries). The time period T over which a suggested operating schedulefor the energy asset(s) may be determined according to the inventiveconcepts disclosed herein may be a portion of an hour, an hour, a periodof multiple hours, a day, or a period of multiple days, for example(which in some instances may be based, at least in part, on time-varyingwholesale electricity prices on a particular wholesale electricitymarket from which revenue may be generated). Similarly, the suggestedoperating schedule(s) for the energy assets(s) may be determined basedat least in part on wholesale prices of various wholesale electricity“products” offered on the wholesale electricity markets in which theenergy customer may participate (e.g., based on a geographic region inwhich the energy customer is located) to earn energy-related revenue.

In one exemplary implementation, as discussed in greater detail below,the suggested operating schedule for one or more energy assets isdetermined via a mathematical optimization process that reduces a netenergy-related cost to the energy customer over the time period T byincreasing projected energy-related revenue from one or more wholesaleelectricity markets in which the energy customer may participate.

Energy Asset Modeling

To facilitate the mathematical optimization process for generating asuggested operating schedule for one or more energy assets, amathematical model representing the customer's energy asset(s) isformulated and employed in the mathematical optimization process. Theenergy asset model is specified by one or more mathematical functionsfor calculating an energy profile (i.e., electricity use and/orelectricity generation as a function of time over the time period T) forthe asset(s), based on a proposed operating schedule for the asset(s)applied as an input to the model. In one aspect, the mathematicalfunction(s) defining the asset model at least in part represent physicalattributes of the energy asset(s) themselves that relate to electricityuse and/or electricity generation. Depending on the energy asset(s)operated by the energy customer, a given model may represent a singleenergy asset or an aggregation of multiple energy assets operated by thecustomer.

Also, depending on the type of energy asset(s) being modeled, the assetmodel may be formulated to accept additional inputs to facilitatecalculation of an energy profile based on a proposed operating schedule.Herein, in various examples, energy storage assets, energy consumingassets and/or energy generating assets are being modeled. For example,in the case of energy consuming assets such as building assets includingheating, ventilation and air conditioning (HVAC) systems for temperaturecontrol in one or more buildings, and/or other assets for whichthermodynamic considerations are relevant (including weather- ortemperature-dependent energy generating assets including photovoltaiccells and wind turbines), the mathematical model for the asset(s) may beconfigured to consider as an input to the model actual or forecastambient environmental conditions (e.g., temperature, humidity, ambientlight/cloud cover, etc.) as a function of time, as well as othervariables that may impact thermodynamics or the energy profile ingeneral (e.g., building occupancy, a presence of equipment such ascomputers and other instrumentation that may affect heating or coolingin an environment, etc.).

Customer Baseline (CBL) Energy Profiles for Business-As-Usual (BAU)Operating Schedules

In some examples, the mathematical model for the energy asset(s) firstis used to generate a simulated (or “predictive”) customer baseline(CBL) energy profile corresponding to a typical operating schedule (alsoreferred to herein as a “business-as-usual” (BAU) operating schedule, or“BAU conditions”). In particular, an energy customer's BAU operatingschedule for its energy asset(s) is applied to the mathematical model,which in turn provides as an output a simulated CBL energy profilerepresenting a typical electricity consumption or generation as afunction of time, over a given time period T, for the modeled energyasset(s). In one aspect, the energy customer's BAU operating schedulerepresents the customer's typical behavior with respect to operating itsenergy asset(s), absent any incentive to reduce energy costs and/or earnenergy-related revenue from the wholesale electricity market.

As discussed in greater detail below, a simulated and predictive CBLenergy profile based on a mathematical model according to the conceptsdisclosed herein provides a significant improvement over conventionalapproaches to determine a frame of reference for typical energy profilesof energy customers (absent an incentive to generate revenue viawholesale electricity markets); as noted above, conventional approachesare limited to considering only historical actual energy useinformation. In particular, the Inventors have recognized andappreciated that conventional backward-looking assessment of CBL is notnecessarily representative of what an energy customer's electricityusage actually would have been on a given day for which economic demandresponse revenue is being calculated—at best, such backward-lookinghistorical actual-use-based assessments of CBL provide inconclusiveestimates.

Additionally, it has been observed empirically that an historicalactual-use CBL provides incentives for some energy customers toartificially inflate energy usage (i.e., by not operating energy assetspursuant to “business-as-usual” or BAU conditions, but insteadpurposefully adopting higher-consumption operating conditions) prior toa period in which the customer anticipates participation in economicdemand response wholesale electricity markets; an artificially higherhistoric actual-use-based CBL, against which energy use reduction willbe measured, provides a potentially higher economic demand responserevenue. In this manner, the general goal of economic demand responseprograms to incentivize reduced electricity usage is undermined (by anartificially-increased electricity usage to establish a higher CBL).

Furthermore, the Inventors have recognized and appreciated that anhistorical actual-use-based CBL provides a long-term disincentive toparticipate in economic demand response wholesale electricity markets.In particular, as a given energy customer participates in economicdemand response wholesale electricity markets over time, their averageactual electricity use from retail suppliers is expected to decrease. Ifrevenue from such markets continues to be calculated with reference toan historical actual-use-based CBL, the potential for economic demandresponse revenue will decrease over time, as an economic settlementapproach based on historical actual-use CBL eventually will begin totreat incentivized electricity use reduction as “business-as-usual”operating conditions for the energy customer. This type of treatmentarguably will ultimately discourage participation in wholesaleelectricity markets. At very least, continued reliance on historicalactual-use-based CBL likely will compel an extension of a “look-back”period serving as a basis for determining CBL for energy customers whoactively participate in economic demand response wholesale electricitymarkets for significant periods of time. If/as longer look-back periodsare adopted, the accuracy and relevance of historic actual-use-basedCBLs from more distant time periods arguably will significantlydecrease.

Accordingly, for at least the foregoing reasons, a simulated andpredictive CBL energy profile, based on a mathematical model of anenergy customer's energy asset(s) according to the concepts disclosedherein (rather than an historical actual-use-based CBL as conventionallyemployed), provides a significant improvement for more accuratelydetermining revenue earned from economic demand response wholesaleelectricity markets. In some examples, the mathematical model for theenergy asset(s) may not be predicated on any significantly historicalactual electricity use information for the energy asset(s), and insteadmay be based primarily on physical attributes of the energy asset(s)themselves that relate to electricity use and/or electricity generation,as noted above. In this manner, simulated and predictive CBL energyprofiles based on such mathematical models are not substantivelyinfluenced by significantly historical actual electricity useinformation.

In other examples, the mathematical model for energy asset(s) may bepredicated on some degree of essentially real-time or near real-timefeedback (e.g., from one or more control systems actually controllingthe modeled energy asset(s)), which feedback may represent actualelectricity use. This feedback may be used, according to some examplesof the methods, apparatus and systems disclosed herein, to refine someaspects of the mathematical model; however, even when real-time or nearreal-time feedback representing actual electricity use is employed, insome examples the mathematical model is still based primarily onphysical attributes of the energy asset(s) themselves relating toelectricity use and/or electricity generation.

Objective Cost Functions

In some examples, the mathematical model for the energy asset(s) isemployed to determine a suggested operating schedule over a given timeperiod T for the energy asset(s) (different than the BAU operatingschedule) based on a mathematical optimization of an “objective costfunction” representing the net energy-related cost to the energycustomer for operating the asset(s). In exemplary implementations, theobjective cost function incorporates the mathematical model for theenergy asset(s) and specifies energy-related revenues from one or morewholesale energy markets (e.g., based on forecasted wholesale energyprices over the time period T for the one or more wholesale markets ofinterest), from which possible revenue may be available to the energycustomer. In some examples, the energy-related revenues specified in theobjective cost function may take into consideration a simulated customerbaseline (CBL) energy profile (discussed above) as a basis fordetermining such revenue.

The objective cost function employed in the mathematical optimization todetermine a suggested operating schedule for the energy asset(s) alsomay specify energy-related costs which are offset by the energy-relatedrevenues. In particular, in some examples, the energy-related costsincluded in the objective cost function may include “actual”energy-related costs (e.g., retail electricity costs, wholesaleelectricity costs representing revenue earned by the energy customer,fuel costs to run one or more electricity generation assets, operationand/or maintenance costs that may be associated with electricitygeneration and/or energy storage assets, lifetime and/or replacementcosts for electricity generation and/or energy storage assets,emissions-related costs, etc.). The energy-related costs included in theobjective cost function additionally or alternatively may include“indirect” energy-related costs, such as convenience/comfort costsassociated with the energy customer's adoption of a suggested operatingschedule different than the BAU operating schedule (theconvenience/comfort cost represents an “indirect” cost associated with achange in the customer's behavior with respect to operating itsasset(s), based on the incentive of possible energy-related revenue fromthe wholesale electricity markets).

Optimization of Objective Cost Function for Generating Energy AssetOperating Schedules

In one example, the objective cost function (which incorporates themathematical model of the energy asset(s)) may be provided to anoptimizer (a particularly-programmed processor, also referred to as a“solver”) that implements a mathematical optimization process todetermine a suggested operating schedule for the energy asset(s) over agiven time period T. In one conceptual illustration of the mathematicaloptimization process, some number N of candidate operating schedules aresuccessively applied to the mathematical model to generate simulatedenergy profiles corresponding to the candidate operating schedules. Anet energy-related cost represented by the objective cost function iscalculated for each simulated energy profile, and the candidateoperating schedule that minimizes the objective cost function (i.e.,minimizes the net energy-related cost) is selected as the suggestedoperating schedule. In some implementations, the amount of revenueavailable from the relevant wholesale electricity markets over the giventime period T is a significant factor dictating the candidate operatingschedule that is provided as an output of the optimizer.

Adopting Operating Schedules, Market Bids and Settlement

The suggested operating schedule in turn may be transmitted to theenergy customer (e.g., to an energy management system and/or buildingmanagement system of the energy customer), and the customer may chooseto adopt or not adopt the suggested operating schedule to actuallyoperate its energy asset(s) over the particular time period T for whichthe optimization is performed. In some implementations, a givenoperating schedule is transmitted to the energy customer in the form ofone or more bias signals representing a change in an operating set pointof one or more assets, as a function of time over the time period T,from the typical or “business-as-usual” (BAU) operating set point forthe asset(s). In some examples, the energy customer makes a choice toadopt a given suggested operating schedule in tandem with making anoffer (a “bid”) to provide one or more wholesale electricity marketproducts to the appropriate market pursuant to the adopted operatingschedule.

If the energy customer adopts the suggested operating schedule toactually operate its energy asset(s) so as to provide a particularwholesale electricity market product pursuant to an accepted bid (e.g.,reduce its energy consumption), various information ultimately isobtained from the energy customer to facilitate a “settlement” processpursuant to which the customer is paid by the wholesale market operator(i.e., the RTO/ISO overseeing the wholesale electricity market(s) inwhich the customer is participating). For example, in one examplerelating to energy markets (wherein the “product” is energy usecurtailment), the energy customer's “metered load” (i.e., actual energyuse during the time period T in which the suggested operating scheduleis adopted) is measured, and compared to a simulated CBL based on themathematical model for the customer's energy asset(s). The energycustomer may then be paid for its economic demand response electricityuse reduction based on a difference between the simulated CBL and theactual metered load, multiplied by the actual wholesale energy priceduring the time period T for the market in question (e.g., LMP).

Apparatuses, methods and computer-readable media are described fordetermining an operating schedule of a controller of at least one energystorage asset operated by an energy customer of an electricity supplier,so as to generate energy-related revenue, over a time period T,associated with operation of the at least one energy storage assetaccording to the operating schedule, wherein the energy-related revenueavailable to the energy customer over the time period T is based atleast in part on a wholesale electricity market. The apparatus includesat least one communication interface, at least one memory to storeprocessor-executable instructions and a mathematical model for the atleast one energy storage asset, and at least one processing unit. Themathematical model facilitates a determination of the operating schedulefor the controller of the at least one energy storage asset based atleast in part on a first operation characteristic of the at least oneenergy storage asset, a second operation characteristic of at least oneenergy consuming asset in communication with the at least one energystorage asset, and a forecast wholesale electricity price associatedwith the wholesale electricity market. The at least one processing unitis communicatively coupled to the at least one communication interfaceand the at least one memory. Upon execution of the processor-executableinstructions, the at least one processing unit determines the operatingschedule for the controller of the at least one energy storage assetusing the mathematical model, and controls the at least onecommunication interface to transmit to the energy customer thedetermined operating schedule for the controller of the at least oneenergy storage asset, and/or controls the at least one memory so as tostore the determined operating schedule for the controller.

In an aspect, upon execution of the processor-executable instructions,the at least one processing unit determines the operating schedule forthe controller of the at least one energy storage asset using themathematical model by minimizing a net energy-related cost over the timeperiod T. The net-energy related cost is based at least in part onelectricity generation by the at least one energy storage asset, firstelectricity consumption by the at least one energy storage asset, andsecond electricity consumption by the at least one energy consumingasset. The energy-related revenue available to the energy customer isbased at least in part on the minimized net energy-related cost.

Apparatuses, methods and computer-readable media are also described fordetermining an operating schedule of a controller of at least one energystorage asset operated by an energy customer of an electricity supplier,so as to generate energy-related revenue, over a time period T,associated with operation of the at least one energy storage assetaccording to the operating schedule, wherein the energy-related revenueavailable to the energy customer over the time period T is based atleast in part on a wholesale electricity market. The apparatus includesat least one communication interface, at least one memory to storeprocessor-executable instructions and a mathematical model for the atleast one energy storage asset, and at least one processing unit. Themathematical model facilitates a determination of the operating schedulefor the controller of the at least one energy storage asset based atleast in part on a first operation characteristic of the at least oneenergy storage asset, a second operation characteristic of at least oneenergy consuming asset in communication with the at least one energystorage asset, and a forecast wholesale electricity price associatedwith the wholesale electricity market. Upon execution of theprocessor-executable instructions, the at least one processing unitdetermines the operating schedule for the controller of the at least oneenergy storage asset using the mathematical model, where the operatingschedule for the controller of the at least one energy storage assetspecifies, during a time interval less than time period T, a proportionof an available state of charge (SOC) of the energy storage asset foruse in an energy market and a remaining proportion of the available SOCof the energy storage asset for use in a regulation market, and controlsthe at least one communication interface to transmit to the energycustomer the determined operating schedule for the controller of the atleast one energy storage asset, and/or controls the at least one memoryso as to store the determined operating schedule for the controller.

In an aspect, upon execution of the processor-executable instructions,the at least one processing unit determines the operating schedule forthe controller of the at least one energy storage asset using themathematical model by minimizing a net energy-related cost over the timeperiod T, where the net-energy related cost is based at least in part onelectricity generation by the at least one energy storage asset, firstelectricity consumption by the at least one energy storage asset, andsecond electricity consumption by the at least one energy consumingasset. The energy-related revenue available to the energy customer isbased at least in part on the minimized net energy-related cost.

Apparatuses, methods and computer-readable media described herein may beused to implement the virtual partitioning and dynamic virtualizationdescribed herein. In this aspect, the at least one memory is configuredto store processor-executable instructions and a mathematical model forthe at least one energy storage asset, where the mathematical modeldetermines the operating schedule for the controller based on dataassociated with parameters, including but not limited to, an operationcharacteristic of the energy storage asset, an operation characteristicof the energy consuming asset in communication with the at least oneenergy storage asset, and a forecast wholesale electricity priceassociated with the wholesale electricity market.

In aspect of virtual partitioning, the at least one processing unitexecutes the processor-executable instructions stored in the memory atleast to determine the operating schedule for the controller of theenergy storage asset using the mathematical model, where the operatingschedule specifies, during a time interval less than time period T, aproportion of an available state of charge (SOC) of the energy storageasset for use in the energy market and a remaining proportion of theavailable SOC of the energy storage asset for use in the regulationmarket. The at least one processing unit also executesprocessor-executable instructions 14 to control the communicationinterface to transmit to the energy customer the operating schedule thathas been determined for the controller and/or controls the memory tostore the determined operating schedule for the controller. In anon-limiting example, the processing unit may executeprocessor-executable instructions to control the communication interfaceto transmit to the operating schedule directly to the controller.

Apparatuses, methods and computer-readable media described herein can beused for determining an operating schedule of a controller of at leastone energy storage asset operated by an energy customer of anelectricity supplier, so as to generate energy-related revenue, over atime period T, associated with operation of the at least one energystorage asset according to the operating schedule, wherein theenergy-related revenue available to the energy customer over the timeperiod T is based at least in part on a wholesale electricity market,and wherein the wholesale electricity market includes an energy marketand a regulation market. The apparatus includes at least onecommunication interface, at least one memory to storeprocessor-executable instructions and a mathematical model for the atleast one energy storage asset, and at least one processing unit. Themathematical model facilitates a determination of the operating schedulefor the controller of the at least one energy storage asset based atleast in part on an operation characteristic of the at least one energystorage asset, a forecast wholesale electricity price associated withthe energy market, and a regulation price associated with the regulationmarket. The at least one processing unit is configured to determine theoperating schedule for the controller of the at least one energy storageasset using the mathematical model by minimizing a net energy-relatedcost over the time period T. The net-energy related cost is based atleast in part on the duration of energy storage asset participation inthe regulation market, electricity generation by the at least one energystorage asset, and electricity consumption by the at least one energystorage asset. The energy-related revenue available to the energycustomer is based at least in part on the minimized net energy-relatedcost. The operating schedule specifies, during a time interval withinthe time period T, a first portion of an available output of thecontroller for use in the energy market and a second portion of theavailable output of the controller for use for use in the regulationmarket. The at least one processing unit is also configured to controlthe at least one communication interface to transmit to the energycustomer the operating schedule for the controller of the at least oneenergy storage asset and/or controls the at least one memory so as tostore the determined operating schedule for the controller

Apparatuses, methods and computer-readable media described herein can beused for determining an operating schedule of a controller of at leastone energy storage asset operated by an energy customer of anelectricity supplier, so as to generate energy-related revenue, over atime period T, associated with operation of the at least one energystorage asset according to the operating schedule, wherein theenergy-related revenue available to the energy customer over the timeperiod T is based at least in part on a wholesale electricity market. Inthis example, the apparatus includes at least one communicationinterface, at least one memory to store processor-executableinstructions and a mathematical model for the at least one energystorage asset, and at least one processing unit. The mathematical modelfacilitates determination of the operating schedule for the controllerbased at least in part on an operation characteristic of the at leastone energy storage asset, an expected energy-generating schedule of theenergy generating asset in communication with the energy storage asset,and a forecast wholesale electricity price associated with the wholesaleelectricity market. The at least one processing unit can be configuredto determine the operating schedule for the controller of the at leastone energy storage asset using the mathematical model, and control theat least one communication interface to transmit to the energy customerthe operating schedule for the controller of the at least one energystorage asset and/or controls the at least one memory so as to store thedetermined operating schedule for the controller.

In an aspect, the at least one processing unit is configured todetermine the operating schedule for the controller of the at least oneenergy storage asset using the mathematical model by minimizing a netenergy-related cost over the time period T. The net-energy related costis based at least in part on the amount of energy generation by the atleast one energy generating asset, electricity generation by the atleast one energy storage asset; and electricity consumption by the atleast one energy storage asset. The energy-related revenue available tothe energy customer is based at least in part on the minimized netenergy-related cost. The net energy-related cost may be specified as adifference between an electricity supply cost and an economic demandresponse revenue over the time period T. The energy generating asset maybe a photovoltaic cell, a fuel cell, a gas turbine, a diesel generator,a flywheel, an electric vehicle, or a wind turbine. The operationcharacteristic of the at least one energy storage asset may be a stateof charge, a charge rate, a degree of non-linearity of charge rate adischarge rate, a degree of non-linearity of discharge rate, a roundtrip efficiency, or a degree of life reduction.

Apparatuses, methods and computer-readable media described herein can beused for determining an operating schedule of a controller of at leastone energy storage asset so as to generate energy-related revenue, overa time period T, associated with operation of the at least one energystorage asset according to the operating schedule. The energy-relatedrevenue available to the energy customer over the time period T is basedat least in part on a wholesale electricity market, and the wholesaleelectricity market includes an energy market and a regulation market. Inthis example, the apparatus includes at least one communicationinterface, at least one memory to store processor-executableinstructions and a mathematical model for the at least one energystorage asset, and at least one processing unit. The mathematical modelfacilitates a determination of the operating schedule for the controllerbased at least in part on an operation characteristic of the at leastone energy storage asset, an expected energy-generating schedule of anenergy generating asset in communication with the energy storage asset,a forecast wholesale electricity price associated with the energymarket, and a regulation price associated with the regulation market.The at least one processing unit is configured to determine theoperating schedule for the controller of the at least one energy storageasset using the mathematical model by minimizing a net energy-relatedcost over the time period T. The net-energy related cost is based atleast in part on the amount of energy generation by the at least oneenergy generating asset, duration of energy storage asset participationin the regulation market, electricity generation by the at least oneenergy storage asset and electricity consumption by the at least oneenergy storage asset. The energy-related revenue available to the energycustomer is based at least in part on the minimized net energy-relatedcost. The operating schedule specifies, during a time interval withinthe time period T, a first portion of an available output of thecontroller for use in the energy market and a second portion of theavailable output of the controller for use for use in the regulationmarket. The at least one processing unit is also configured to controlthe at least one communication interface to transmit to the energycustomer the operating schedule for the controller of the at least oneenergy storage asset and/or controls the at least one memory so as tostore the determined operating schedule for the controller.

Apparatuses, methods and computer-readable media described herein can beused for determining an operating schedule of at least one controller ofat least one energy asset as to generate energy-related revenue, over atime period T, associated with operation of the at least one energyasset according to the operating schedule. The energy-related revenueavailable to the energy customer over the time period T is based atleast in part on at least one wholesale electricity market. Theapparatus includes at least one communication interface, at least onememory to store processor-executable instructions and a mathematicalmodel for the at least one energy asset, and at least one processingunit. The mathematical model facilitates a determination of theoperating schedule for the controllers based at least in part on anoperation characteristic of the at least one energy asset and forecastwholesale electricity prices associated with the at least one wholesaleelectricity market. The at least one processing unit is configured todetermine the operating schedule for the at least one controller of theat least one energy storage asset using the mathematical model byminimizing a net energy-related cost over the time period T. Thenet-energy related cost is based at least in part on at least one energysupply cost and at least one demand response revenue. The operatingschedule specifies, during a time interval within the time period T,conditions for use of the at least one energy asset in respective onesof the at least one energy market. The at least one processing unit isalso configured to control the at least one communication interface totransmit to the energy customer the operating schedule for the at leastone controller of the at least one energy asset, control the at leastone memory so as to store the determined operating schedule for the atleast one controller, and/or control the at least one communicationinterface to transmit to the at least one controller of at least oneenergy asset the operating schedule. The energy asset can be at leastone of an energy storage asset, an energy generating asset, an energyconsuming asset, or any combination thereof. The at least one wholesaleelectricity market can be at least one of an energy market, a regulationmarket, a spinning reserve market, or any combination thereof. Theforecast wholesale electricity prices associated with the energy marketcan be a wholesale price. The forecast wholesale electricity pricesassociated with the regulation market can be a regulation price. Theforecast wholesale electricity prices associated with the spinningreserve market can be a spinning reserve market price.

The following patent applications are hereby incorporated herein byreference in their entirety:

U.S. Provisional Application No. 61/477,067, filed on Apr. 19, 2011;

U.S. Provisional Application No. 61/552,982, filed on Oct. 28, 2011;

U.S. Non-provisional application Ser. No. 12/850,918, filed on Aug. 5,2010; and

U.S. Provisional Application No. 61/279,589, filed on Oct. 23, 2009.

The entire disclosure of these applications is incorporated herein byreference in its entirety, including drawings,

It should be appreciated that all combinations of the foregoing conceptsand additional concepts discussed in greater detail below (provided suchconcepts are not mutually inconsistent) are contemplated as being partof the inventive subject matter disclosed herein. In particular, allcombinations of claimed subject matter appearing at the end of thisdisclosure are contemplated as being part of the inventive subjectmatter disclosed herein. It should also be appreciated that terminologyexplicitly employed herein that also may appear in any disclosureincorporated by reference should be accorded a meaning most consistentwith the particular concepts disclosed herein.

BRIEF DESCRIPTION OF THE DRAWINGS

The skilled artisan will understand that the drawings primarily are forillustrative purposes and are not intended to limit the scope of theinventive subject matter described herein. The drawings are notnecessarily to scale; in some instances, various aspects of theinventive subject matter disclosed herein may be shown exaggerated orenlarged in the drawings to facilitate an understanding of differentfeatures. In the drawings, like reference characters generally refer tolike features (e.g., functionally similar and/or structurally similarelements).

FIG. 1 shows an example system that includes an energy storage asset, acontroller, and an energy consuming asset, according to a principledescribed herein.

FIG. 2 shows an example apparatus according to a principle describedherein.

FIG. 3 shows an example system that includes an energy storage asset, acontroller, an energy generating asset, and an energy consuming asset,according to a principle described herein.

FIG. 4 shows an example system that includes an energy storage asset, acontroller, and an energy generating asset, according to a principledescribed herein.

FIG. 5 shows an example system that includes an energy storage asset anda controller, according to a principle described herein.

FIG. 6 illustrates an example block diagram representing an asset modelaccording to a principle described herein.

FIG. 7 illustrates an example block diagram representing another assetmodel according to a principle described herein.

FIG. 8 illustrates an example block diagram representing another assetmodel according to a principle described herein.

FIG. 9 illustrates an example block diagram representing another assetmodel according to a principle described herein.

FIG. 10 illustrates an example block diagram representing another assetmodel according to a principle described herein.

FIG. 11 shows an example of an implementation based on an operatingschedule, according to a principle described herein.

FIG. 12 shows an example energy storage asset optimization according toa principle described herein.

FIG. 13 shows an example generation schedule for an energy storageasset-energy generating asset co-optimization according to a principledescribed herein.

FIGS. 14 and 15 show an example flow chart of a method according to aprinciple described herein.

FIG. 16 shows an example block diagram relating to modeling andoptimization techniques that may be employed in the implementation ofFIGS. 14 and 15, according to a principle described herein.

FIG. 17 shows example details of an optimization technique, according toa principle described herein.

FIG. 18 shows an example system that includes various modules forimplementing the concepts described in connection with FIGS. 14-16,according to a principle described herein.

FIG. 19 shows an example optimization, according to a principledescribed herein.

FIG. 20 shows an example system architecture, according to a principledescribed herein.

FIG. 21 shows example power use and price information for variouselectric energy resources in an optimization case example over a 24-hourcycle as generated according to a principle described herein.

DETAILED DESCRIPTION

Following below are more detailed descriptions of various conceptsrelated to, and embodiments of, inventive methods, apparatus, andsystems for determining a suggested operating schedule for energy assetsto facilitate revenue generation from wholesale electricity markets. Itshould be appreciated that various concepts introduced above anddiscussed in greater detail below may be implemented in any of numerousways, as the disclosed concepts are not limited to any particular mannerof implementation. Examples of specific implementations and applicationsare provided primarily for illustrative purposes.

As used herein, the term “includes” means includes but not limited to,the term “including” means including but not limited to. The term “basedon” means based at least in part on.

The apparatuses and methods described herein are applicable to a systemthat includes an energy storage asset 1, a controller 2 in communicationwith the energy storage asset 1, and an energy consuming asset 3 incommunication with a power line 4 (as depicted in the example of FIG.1). The controller 2 facilitates charging of the energy storage asset 31using the electricity supplied by power line 4 or feeding powergenerated by a discharge of the energy storage asset 31 to the powerline 4. As depicted in the non-limiting example of FIG. 1, thecontroller 2, the energy storage asset 1 and the energy consuming asset3 may be located behind a power meter 5. For example, all of thecontroller 2, the energy storage asset 1 and the energy consuming asset3 may be located at one or more facilities of the energy consumer.

Non-limiting examples of energy storage assets include batteries, iceunits, and compressed air. Non-limiting examples of batteries includelithium ion batteries, lead-acid batteries, flow batteries, or dry celltechnology batteries.

In the non-limiting example of FIG. 1, the controller 2 facilitates thecommunication between the energy consuming asset and the energy storageasset. In another example, the energy consuming asset may communicatewith the energy storage asset via one or more other components includingthe controller 2.

The apparatuses and methods herein facilitate generation ofenergy-related revenue for an energy customer of an electricitysupplier, where the energy customer commits an amount of energy from theat least one energy storage asset to an energy market. In an example,the electricity supplier may be a retail electricity supplier thatsupplies the electricity to the energy customer at a retail price. Inanother example, the electricity supplier may supply the electricity tothe energy customer at a contracted for or negotiated price. In variousexamples herein, the energy customer may allow an amount of capacity ofthe energy storage asset to be committed to the energy market. Whenimplemented, the apparatuses and methods described herein may allow theenergy customer to generate an amount of energy-related revenue over atime period that an amount of capacity of the energy storage asset iscommitted to the energy market.

In a non-limiting example, an apparatus or a method described herein canbe used to generate an operating schedule for a controller thatcommunicates with the energy storage asset. The controller is capable ofexercising an amount of control over the rate of charging or energygeneration of the energy storage asset. As a result, the controller canbe used to maintain the state of charge of the energy storage asset, orchange its state of charge controllably. Operation of the controller,and hence the energy storage asset, according to the operating schedulegenerated by an apparatus or a method herein over the time period maymake available to the energy customer an amount of energy-relatedrevenue based at least in part on a wholesale electricity market.

A non-limiting example of the apparatus 10 according to the principlesdescribed herein is illustrated in FIG. 2. The apparatus 10 includes atleast one communication interface 11, at least one memory 12, and atleast one processing unit 13. The at least one processing unit 13 iscommunicatively coupled to the at least one communication interface 11and the at least one memory 12.

The at least one memory 12 is configured to store processor-executableinstructions 14 and a mathematical model 15 for the at least one energystorage asset. As described in greater detail below, the mathematicalmodel determines the operating schedule for the controller based on data16 associated with parameters, including but not limited to, anoperation characteristic of the energy storage asset, an operationcharacteristic of an energy consuming asset in communication with theenergy storage asset and a forecast wholesale electricity priceassociated with the wholesale electricity market.

In a non-limiting example, the at least one processing unit 13 executesthe processor-executable instructions 14 stored in the memory 12 atleast to determine the operating schedule for the controller of theenergy storage asset using the mathematical model 15. The at least oneprocessing unit 13 also executes processor-executable instructions 14 tocontrol the communication interface 11 to transmit to the energycustomer 17 the operating schedule that has been determined for thecontroller and/or controls the memory 12 to store the determinedoperating schedule for the controller. In a non-limiting example, theprocessing unit 13 may execute processor-executable instructions 14 tocontrol the communication interface 11 to transmit to the operatingschedule directly to the controller.

The operation characteristic of the energy storage asset may be itsstate of charge, charge rate, the degree of non-linearity of the chargerate, discharge rate, degree of non-linearity of the discharge rate,round trip efficiency, and degree of life reduction. In an example wherethe operation characteristic of the energy storage asset is its chargerate and/or discharge rate, the operating schedule for the controllermay include suggested different time intervals for charging the energystorage asset or discharging the energy storage asset during the timeperiod T that the system is in operation. As a non-limiting example, theoperating schedule for the controller may indicate a time interval forcharging the energy storage asset that coincides with a correspondingtime interval during which the forecast wholesale electricity pricefalls below a predetermined threshold value. As another non-limitingexample, the operating schedule for the controller may indicate a timeinterval of discharging the energy storage asset that coincides with acorresponding time interval during which the forecast wholesaleelectricity price exceeds a predetermined threshold value.

The operation characteristic of the energy consuming asset may be itsload use schedule. For example, the operation characteristic of theenergy consuming asset can be its energy consumption profile as afunction of time. The energy consuming asset may be a controllable assetor a fixed-load asset. A fixed-load asset is an energy consuming assetwhose energy consumption characteristics may not be readily modified,even if it varies over time. The energy consumption characteristics of acontrollable energy consuming asset may be modified by changingparameters of operation of the system. A non-limiting example of anoperation characteristic for a controllable energy consuming asset isits set point. The set point may be a controllable set point, e.g., itmay be controllable as a function of time or temperature. For example,where the controllable energy consuming asset is a building with avariable internal temperature controlled by a heating, ventilation andair conditioning (HVAC) system, the operation characteristic may be atemperature set point for the HVAC system.

As described herein, in an example, an amount of energy of the energystorage asset may be generated and supplied to the power line at adischarge rate to generate energy-related revenue for the energycustomer in an energy market. The energy-related revenue can depend on aforecast wholesale electricity price associated with the wholesaleelectricity market, and may be determined based on computation of anet-energy related cost. The net energy related cost may be computedbased on the supply costs for supplying electricity to the customer anda demand response revenue. An apparatus and method herein can beimplemented to generate an operating schedule for the controller of theenergy storage asset that provides recommendations for the timing ofcharging and discharging of the energy storage asset.

In an example, the processing unit can be configured to determine theoperating schedule for the controller of the at least one energy storageasset using the mathematical model by minimizing a net energy-relatedcost over the relevant time period (T). The net energy-related cost canbe associated with electricity generation by the energy storage asset,electricity consumption by the energy storage asset, and electricityconsumption by the energy consuming asset. Here, the energy-relatedrevenue available to the energy customer may be computed based at leastin part on the minimized net energy-related cost.

The net energy-related cost may be specified as a difference between theelectricity supply cost and the economic demand response revenue overthe pertinent time period.

In an example, the processing unit can be configured to determine theoperating schedule for the controller using the mathematical model and arepresentative customer baseline (CBL) energy profile for the energyconsuming asset over the time period (T). As used herein, the term“representative customer baseline energy profile” or “representative CBLenergy profile” encompasses representations of the energy customer'senergy usage in the absence of change of behavior according to theprinciples described herein. As non-limiting examples, the“representative customer baseline energy profile” or “representative CBLenergy profile” includes an estimation based on the energy customer'sbusiness-as-usual (BAU) operations, including any form of averaged orweighted measure based on measures of historical BAU operations. Herein,the representative CBL energy profile represents a typical operation ofthe at least one energy consuming asset by the energy customer. Forexample, where the energy consuming asset is a fixed-load asset, therepresentative CBL may be determined as the energy consumption profilefor the energy consuming asset.

Where the operating schedule for the controller is generated based onusing the mathematical model and a representative customer baseline(CBL) energy profile, the economic demand response revenue may becomputed based on the forecast wholesale electricity price, theelectricity generation by the energy storage asset, the electricityconsumption by the energy storage asset, and the representative CBLenergy profile for the energy consuming asset.

In an example herein, a portion of the energy of the energy storageasset may be committed to the regulation market. That is, the wholesaleelectricity market for the energy customer would include an energymarket and a regulation market. In an example where the forecastwholesale electricity price is for the energy market, the operatingschedule for the controller may specify optimal time intervals for useof the energy storage asset in the regulation market. For example, ifthe forecast wholesale electricity price for the energy market isprojected to fall below a predetermined threshold value during a timeinterval, the operating schedule for the controller may recommend of theenergy storage asset in the regulation market during that time interval.Where the forecast wholesale electricity price for the energy market isprojected to fall below a predetermined threshold value during a timeinterval, the operating schedule for the controller may recommend use ofthe energy storage asset in the regulation market during that timeinterval.

According to an example of the principles herein, the wholesaleelectricity market may include both the energy market and the regulationmarket, and the operating schedule generated may facilitateimplementation of the energy storage asset in both the energy market andthe regulation market. According to a principle of virtual partitioningdescribed herein, the operating schedule for the controller may beconfigured so that the energy customer may participate in both theenergy market and the regulation market concurrently the energy storageasset. In a non-limiting example, the operating schedule for thecontroller of the energy storage asset may specify that, during a giventime interval, a first portion of an available state of charge (SOC) ofthe energy storage asset may be used in the energy market and a secondportion of the available SOC of the energy storage asset may becommitted to the regulation market. The operating schedule generate forthe controller may be used to energy-related revenue for the energyconsumer based on both the energy market and the regulation market. Theprinciples and implementations described above in connection to FIG. 1are also applicable to a system operating according to the principles ofvirtual partitioning.

The apparatus 10 illustrated in FIG. 2 may be used to implement thevirtual partitioning described herein. In this non-limiting example, theat least one memory 12 is configured to store processor-executableinstructions 14 and a mathematical model 15 for the at least one energystorage asset, where the mathematical model determines the operatingschedule for the controller based on data 16 associated with parameters,including but not limited to, an operation characteristic of the energystorage asset, an operation characteristic of the energy consuming assetin communication with the at least one energy storage asset, and aforecast wholesale electricity price associated with the wholesaleelectricity market.

In this non-limiting example of virtual partitioning, the at least oneprocessing unit 13 executes the processor-executable instructions 14stored in the memory 12 at least to determine the operating schedule forthe controller of the energy storage asset using the mathematical model15, where the operating schedule specifies, during a time interval lessthan time period T, a proportion of an available state of charge (SOC)of the energy storage asset for use in the energy market and a remainingproportion of the available SOC of the energy storage asset for use inthe regulation market. The at least one processing unit 13 also executesprocessor-executable instructions 14 to control the communicationinterface 11 to transmit to the energy customer 17 the operatingschedule that has been determined for the controller and/or controls thememory 12 to store the determined operating schedule for the controller.In a non-limiting example, the processing unit 13 may executeprocessor-executable instructions 14 to control the communicationinterface 11 to transmit to the operating schedule directly to thecontroller.

In a non-limiting example, the operation characteristic of the at leastone energy storage asset can be at least one of a state of charge, acharge rate, a degree of non-linearity of charge rate a discharge rate,a degree of non-linearity of discharge rate, a round trip efficiency,and a degree of life reduction. The proportion of the available SOC ofthe energy storage asset for use in the energy market may be supplied asa direct-current (DC) signal, while the remaining proportion of theavailable SOC of the energy storage asset for use in the regulationmarket may be delivered at a variable charge rate or variable dischargerate.

In an example where the energy storage asset is used in both the energymarket and the regulation market, constraints may be placed on the totalamount of energy used. For example, the total SOC of the energy storageasset over the time that it is used in both markets can be constrainedto be depleted to no less than a minimum allowed SOC value or charged tono more than a maximal allowed SOC value. In an example, the sum of theproportion of the available SOC of the at least one energy storage assetfor use in the energy market and the remaining proportion of theavailable SOC of the at least one energy storage asset for use in theregulation market can be constrained to be no less than a minimalallowed SOC and no more than a maximal allowed SOC. As a non-limitingexample, the maximal allowed SOC of the energy storage asset may be setat 80%, and the minimal allowed SOC may be set at 20%.

The apparatuses and methods described herein are also applicable to asystem as depicted in the example of FIG. 3. In this example, theapparatus includes an energy storage asset 31, a controller 32 incommunication with the energy storage asset 31, an energy generatingasset 33 and an energy consuming asset 34 in communication with a powerline 35. The controller 32 in communication with the energy storageasset 31 facilitates charging of the energy storage asset 31 using theelectricity supplied by power line 35. The controller 32 alsofacilitates feeding power generated by a discharge of the energy storageasset 31 to the power line 35. Non-limiting examples of energygenerating assets include photovoltaic cells, fuel cells, gas turbines,diesel generators, flywheels, electric vehicles, and wind turbines. Asdepicted in the non-limiting example of FIG. 1, the controller 32, theenergy storage asset 31, the energy generating asset 33, and the energyconsuming asset 34 may be located behind a power meter 35. For example,all of the controller 32, the energy storage asset 31, the energygenerating asset 33, and the energy consuming asset 34 may be located atone or more facilities of the energy consumer.

In the non-limiting example of FIG. 3, the controller 32 facilitates thecommunication between the energy consuming asset, the energy storageasset, and the energy generating asset. In other examples, the energyconsuming asset may communicate with the energy storage asset via one ormore other components including the controller 32.

An apparatus according to the principles of FIG. 2 may be implementedrelative to the system of FIG. 3 to generate an operating schedule forthe controller 32. In this example, the mathematical model facilitatesdetermination of the operating schedule for the controller of the atleast one energy storage asset further based at least in part on anexpected energy-generating schedule of the energy generating asset incommunication with the energy storage asset and the energy consumingasset. Any principles and/or implementations described herein, includingabove, in connection with FIG. 1 are also applicable to the system ofFIG. 3.

The apparatuses and methods described herein are also applicable to asystem as depicted in the example of FIG. 4. In this example, theapparatus includes an energy storage asset 41, a controller 42 incommunication with the energy storage asset 41, and an energy generatingasset 43 in communication with a power line 44. The controller 42facilitates charging of the energy storage asset 31 using theelectricity supplied by power line 44. The controller 42 alsofacilitates feeding power generated by a discharge of the energy storageasset 41 to the power line 44. Non-limiting examples of energygenerating assets include photovoltaic cells, fuel cells, gas turbines,diesel generators, flywheels, electric vehicles, and wind turbines. Asdepicted in the non-limiting example of FIG. 4, the controller 42, theenergy storage asset 41, and the energy generating asset 43 may belocated behind a power meter 45. For example, all of the controller 42,the energy storage asset 41, and the energy generating asset 33 may belocated at one or more facilities of the energy consumer.

In the non-limiting example of FIG. 4, the controller 42 facilitates thecommunication between the energy storage asset and the energy generatingasset. In other examples, the energy consuming asset may communicatewith the energy storage asset via one or more other components includingthe controller 42.

An apparatus according to the principles of FIG. 2 may be implementedrelative to the system of FIG. 4 to generate an operating schedule forthe controller 42. In this example, the mathematical model facilitatesdetermination of the operating schedule for the controller of the atleast one energy storage asset further based at least in part on anexpected energy-generating schedule of the energy generating asset incommunication with the energy storage asset. Any principles and/orimplementations described herein, including above, in connection withFIG. 1 are also applicable to the system of FIG. 4.

In a non-limiting example, the apparatus of FIG. 2 can be used fordetermining an operating schedule of a controller of at least one energystorage asset operated by an energy customer of an electricity supplier,so as to generate energy-related revenue, over a time period T,associated with operation of the at least one energy storage assetaccording to the operating schedule, wherein the energy-related revenueavailable to the energy customer over the time period T is based atleast in part on a wholesale electricity market. In this example, theapparatus includes at least one communication interface, at least onememory to store processor-executable instructions and a mathematicalmodel for the at least one energy storage asset, and at least oneprocessing unit. The mathematical model facilitates determination of theoperating schedule for the controller based at least in part on anoperation characteristic of the at least one energy storage asset, anexpected energy-generating schedule of the energy generating asset incommunication with the energy storage asset, and a forecast wholesaleelectricity price associated with the wholesale electricity market. Theat least one processing unit can be configured to determine theoperating schedule for the controller of the at least one energy storageasset using the mathematical model, and control the at least onecommunication interface to transmit to the energy customer the operatingschedule for the controller of the at least one energy storage assetand/or controls the at least one memory so as to store the determinedoperating schedule for the controller.

In this example, the at least one processing unit can be configured todetermine the operating schedule for the controller of the at least oneenergy storage asset using the mathematical model by minimizing a netenergy-related cost over the time period T. The net-energy related costis based at least in part on the amount of energy generation by the atleast one energy generating asset, electricity generation by the atleast one energy storage asset; and electricity consumption by the atleast one energy storage asset. The energy-related revenue available tothe energy customer is based at least in part on the minimized netenergy-related cost. The net energy-related cost may be specified as adifference between an electricity supply cost and an economic demandresponse revenue over the time period T. The energy generating asset maybe a photovoltaic cell, a fuel cell, a gas turbine, a diesel generator,a flywheel, an electric vehicle, or a wind turbine. The operationcharacteristic of the at least one energy storage asset may be a stateof charge, a charge rate, a degree of non-linearity of charge rate adischarge rate, a degree of non-linearity of discharge rate, a roundtrip efficiency, or a degree of life reduction.

In another non-limiting example, the apparatus of FIG. 2 can be used fordetermining an operating schedule of a controller of at least one energystorage asset operated by an energy customer of an electricity supplier,so as to generate energy-related revenue, over a time period T,associated with operation of the at least one energy storage assetaccording to the operating schedule. The energy-related revenueavailable to the energy customer over the time period T is based atleast in part on a wholesale electricity market, and the wholesaleelectricity market includes an energy market and a regulation market. Inthis example, the apparatus includes at least one communicationinterface, at least one memory to store processor-executableinstructions and a mathematical model for the at least one energystorage asset, and at least one processing unit. The mathematical modelfacilitates a determination of the operating schedule for the controllerbased at least in part on an operation characteristic of the at leastone energy storage asset, an expected energy-generating schedule of anenergy generating asset in communication with the energy storage asset,a forecast wholesale electricity price associated with the energymarket, and a regulation price associated with the regulation market.The at least one processing unit is configured to determine theoperating schedule for the controller of the at least one energy storageasset using the mathematical model by minimizing a net energy-relatedcost over the time period T. The net-energy related cost is based atleast in part on the amount of energy generation by the at least oneenergy generating asset, duration of energy storage asset participationin the regulation market, electricity generation by the at least oneenergy storage asset and electricity consumption by the at least oneenergy storage asset. The energy-related revenue available to the energycustomer is based at least in part on the minimized net energy-relatedcost. The operating schedule specifies, during a time interval withinthe time period T, a first portion of an available output of thecontroller for use in the energy market and a second portion of theavailable output of the controller for use for use in the regulationmarket. The at least one processing unit is also configured to controlthe at least one communication interface to transmit to the energycustomer the operating schedule for the controller of the at least oneenergy storage asset and/or controls the at least one memory so as tostore the determined operating schedule for the controller.

In this example, the available output of the controller may be a chargerate of the at least one energy storage asset or a discharge rate of theat least one energy storage asset. The net energy-related cost isspecified as a difference between an electricity supply cost and aneconomic demand response revenue over the time period T. The operationcharacteristic of the at least one energy storage asset may be a stateof charge, a charge rate, a degree of non-linearity of charge rate adischarge rate, a degree of non-linearity of discharge rate, a roundtrip efficiency, and a degree of life reduction.

The apparatuses and methods described herein are also applicable to asystem as depicted in the example of FIG. 5. In this example, theapparatus includes an energy storage asset 51, and a controller 52 incommunication with the energy storage asset 51 and in communication witha power line 54. The controller 52 facilitates charging of the energystorage asset 31 using the electricity supplied by power line 54. Thecontroller 52 also facilitates feeding power generated by a discharge ofthe energy storage asset 51 to the power line 54. Non-limiting examplesof energy generating assets include photovoltaic cells, fuel cells, gasturbines, diesel generators, flywheels, electric vehicles, and windturbines. As depicted in the non-limiting example of FIG. 5, thecontroller 52, and the energy storage asset 51 may be located behind apower meter 53. For example, the controller 52 and the energy storageasset 51 may be located at one or more facilities of the energyconsumer.

In the non-limiting example of FIG. 5, the controller 52 facilitates thecommunication between the energy storage asset and the energy generatingasset. In other examples, the energy consuming asset may communicatewith the energy storage asset via one or more other components includingthe controller 52.

An apparatus according to the principles of FIG. 2 may be implementedrelative to the system of FIG. 5 to generate an operating schedule forthe controller 52. In this example, the mathematical model facilitatesdetermination of the operating schedule for the controller of the atleast one energy storage asset further based at least in part on anexpected energy-generating schedule of the energy generating asset incommunication with the energy storage asset. Any principles and/orimplementations described herein, including above, in connection withFIG. 1 are also applicable to the system of FIG. 5.

In another non-limiting example, the apparatus of FIG. 2 can be used fordetermining an operating schedule of a controller of at least one energystorage asset operated by an energy customer of an electricity supplier,so as to generate energy-related revenue, over a time period T,associated with operation of the at least one energy storage assetaccording to the operating schedule, wherein the energy-related revenueavailable to the energy customer over the time period T is based atleast in part on a wholesale electricity market, and wherein thewholesale electricity market includes an energy market and a regulationmarket. The apparatus includes at least one communication interface, atleast one memory to store processor-executable instructions and amathematical model for the at least one energy storage asset, and atleast one processing unit. The mathematical model facilitates adetermination of the operating schedule for the controller of the atleast one energy storage asset based at least in part on an operationcharacteristic of the at least one energy storage asset, a forecastwholesale electricity price associated with the energy market, and aregulation price associated with the regulation market. The at least oneprocessing unit is configured to determine the operating schedule forthe controller of the at least one energy storage asset using themathematical model by minimizing a net energy-related cost over the timeperiod T. The net-energy related cost is based at least in part on theduration of energy storage asset participation in the regulation market,electricity generation by the at least one energy storage asset, andelectricity consumption by the at least one energy storage asset. Theenergy-related revenue available to the energy customer is based atleast in part on the minimized net energy-related cost. The operatingschedule specifies, during a time interval within the time period T, afirst portion of an available output of the controller for use in theenergy market and a second portion of the available output of thecontroller for use for use in the regulation market. The at least oneprocessing unit is also configured to control the at least onecommunication interface to transmit to the energy customer the operatingschedule for the controller of the at least one energy storage assetand/or controls the at least one memory so as to store the determinedoperating schedule for the controller.

In this example, the available output of the controller is a charge rateof the at least one energy storage asset or a discharge rate of the atleast one energy storage asset. The net energy-related cost may bespecified as a difference between an electricity supply cost and aneconomic demand response revenue over the time period T. The operationcharacteristic of the at least one energy storage asset is a state ofcharge, a charge rate, a degree of non-linearity of charge rate adischarge rate, a degree of non-linearity of discharge rate, a roundtrip efficiency, or a degree of life reduction.

Energy Asset Modeling

To facilitate the mathematical optimization process for generating asuggested operating schedule for one or more energy assets according tovarious examples of the principles herein, a mathematical modelrepresenting an energy customer's energy asset(s) is formulated andemployed to simulate an “energy profile” for the asset(s). In oneaspect, the model is essentially specified by one or more mathematicalfunctions that at least in part represent physical attributes of theenergy asset(s) themselves as they relate to electricity use and/orelectricity generation. Depending on the energy asset(s) operated by theenergy customer, the mathematical function(s) defining an asset modelmay represent a single energy asset or an aggregation of multiple energyassets operated by the customer. For purposes of the discussion herein,the term “asset model,” unless otherwise qualified, is used generally todenote a model representing either a single energy asset or anaggregation of multiple energy assets.

To illustrate the general concept of an asset model, a model is firstconsidered for one or more energy assets that not only may be turned“on” or “off,” but that may be controlled at various “operating setpoints.” For example, consider the case of a “building asset,” e.g., oneor more buildings including a heating, ventilation and air conditioning(HVAC) system for temperature control, for which the customer may choosedifferent temperature set points at different times (e.g., thermostatsettings); accordingly, in this example, the temperature set pointsconstitute “operating set points” of the building asset. In thisexample, the magnitude of the operating set point may vary as a functionof time t, in a continuous or step-wise manner (e.g., Temp(t)=72 degreesF. for 9 PM<t<9 AM; Temp(t)=68 degrees F. for 9 AM<t<9 PM). In otherexamples of energy assets that merely may be turned “on” or “off,” themagnitude of the operating set point may be binary (i.e., on or off),but the respective on and off states may vary as a function of time t(e.g., over a given time period T).

Based on the notion of time-varying operating set points for energyassets, the term “operating schedule” as used herein refers to anoperating set point of one or more energy assets as a function of time,and is denoted by the notation SP(t):SP(t)≡operating schedule for one or more energy assets.

The amount of energy used (and/or generated) by a particular asset orgroup of assets in a given time period T is referred to herein as an“energy profile.” In various implementations discussed herein, theenergy profile of one or more assets often depends at least in part on agiven operating schedule SP(t) for the asset(s) during the time periodT. For a fixed-load asset, the energy profile may not depend on a givenoperating schedule SP(t). Accordingly, an energy asset model specifiesone or more mathematical functions for calculating an energy profile(i.e., electricity use and/or electricity generation as a function oftime) for the asset(s), based on a proposed operating schedule for theasset(s) applied as an input to the model. The one or more functionsconstituting the asset model are denoted herein generally as F (and forsimplicity the term “function” when referring to F may be used in thesingular), and the model may be conceptually represented usingmathematical notation as:F(SP(t))=EP(t),  Eq. 1where the operating schedule SP(t) is an argument of the function F, andthe energy profile of the modeled asset(s) as a function of time isdenoted as EP(t). In a non-limiting example, EP(t) has units of MWh.FIG. 6 illustrates a simple block diagram representing the asset modelgiven by Eq. 1.

In various examples, the function(s) F defining a particular asset modelmay be relatively simple or arbitrarily complex functions of theargument SP(t) (e.g., the function(s) may involve one or more constants,have multiple terms with respective coefficients, include terms ofdifferent orders, include differential equations, etc.) to reflect howthe asset(s) consume or generate energy in response to the operatingschedule SP(t). In general, the particular form of a given function F,and/or the coefficients for different terms, may be based at least inpart on one or more physical attributes of the asset(s), and/or theenvironment in which the asset(s) is/are operated, which may impact theenergy profile of the asset(s) pursuant to the operating schedule. Morespecifically, depending on the type of energy asset(s) being modeled,the mathematical model may be formulated to accept other inputs (inaddition to the operating schedule SP(t)), and/or to accommodatevariable parameters of a given function F (e.g., via time-dependentcoefficients of different terms of the function), to facilitatecalculation of the energy profile EP(t) based on a proposed operatingschedule SP(t).

For example, in the case of the building asset discussed above, and/orother assets for which thermodynamic considerations are pertinent,various internal factors that may impact the asset's energy profile ingeneral (e.g., building occupancy; a presence of equipment such ascomputers and other instrumentation that may affect heating or coolingin an environment; thermal inertia due to insulation, buildingmaterials, windows; etc.) may be considered in the formulation of theform of the function F itself, and/or coefficients for different termsof the function F. In some examples discussed in further detail below,the function F may be dynamically adjusted based on observing actualenergy usage over time by the asset(s) pursuant to control via aparticular operating schedule (i.e., coefficients of function termsinitially may be estimated, and subsequently adjusted over time based onreal-time feedback from controlled assets).

Similarly, the mathematical model for the asset(s) may be configured toconsider as an input to the model actual or forecast ambientenvironmental conditions (e.g., temperature, humidity, ambientlight/cloud cover, etc.) as a function of time, collectively denoted as“weather information” W(t), which may impact the energy profile of oneor more assets. In this case, the model may be conceptually representedas:F(SP(t),W(t))=EP(t),  Eq. 2where both the operating schedule SP(t) and the weather information W(t)are arguments of the function F. FIG. 7 illustrates a simple blockdiagram representing the asset model given by Eq. 2. It should beappreciated that, while weather information W(t) is noted above asproviding another possible input to the model in addition to theoperating schedule SP(t), in other examples one or more other inputs tothe model may be provided and considered as arguments to the function F(and accordingly taken into consideration in the function) for purposesof calculating an energy profile EP(t) for the asset(s).

In another example herein, the mathematical model for a system thatincludes a controllable asset, such as an energy storage asset and anassociated controller, may be configured to consider as an input to themodel the control vector for the controller as a function of time,denoted as u(t), which may impact the energy profile. In this case, themodel may be conceptually represented as:F(u(t))=EP(t),  Eq. 3where both the control vector of the controller is an argument of thefunction F. FIG. 8 illustrates a simple block diagram representing theasset model given by Eq. 3. It should be appreciated that, while thecontrol vector u(t) is noted above as providing input to the model, inother examples, one or more other inputs to the model may be providedand considered as arguments to the function F (and accordingly takeninto consideration in the function) for purposes of calculating anenergy profile EP (t) for the asset(s).

In yet another example herein, the mathematical model for a system thatincludes an energy consuming asset, such as but not limited to abuilding, and a controllable asset, such as but not limited to an energystorage asset and an associated controller, may be configured toconsider as an input to the model the control vector for the controlleras a function of time, denoted as u(t), and temperature dependentoperating set points for the energy consuming asset (its operatingschedule). In this case, the model may be conceptually represented as:F(u(t),SP(t))=EP(t),  Eq. 4where both the control vector of the controller is an argument of thefunction F. FIG. 9 illustrates a simple block diagram representing theasset model given by Eq. 4. The control vector for a controller,u(t)=C_(t)+D_(t), may be expressed as:C _(t) =u _(1,t) *C/D _(max)D _(t) =u _(2,t) *C/D _(max)  Eq. 5with the constraints that u_(1,t)*u_(2,t)=0 and 0≦u_(1,t), u_(2,t)≦1,where represents C/D_(max) the maximum charge rate or discharge ratecapacity of the controller in communication with the energy storageasset.

In yet another example herein, the mathematical model for a system thatincludes an energy consuming asset, such as but not limited to abuilding, and a controllable asset, such as but not limited to an energystorage asset and an associated controller, may be configured toconsider as an input to the model the control vector for the controlleras a function of time, denoted as u(t), and temperature dependentoperating set points for the energy consuming asset (its operatingschedule). FIG. 10 illustrates a simple block diagram representing theasset model for such as system according to the principles herein. Inthis case, the model may have outputs of the state of charge (SOC_(t))of the energy storage asset as a function of time t, thereturn-a-temperature (RAT_(t)) as a function of time t (for, e.g., aHVAC or other similar equipment), and the energy profile of the energyconsuming asset (e.g., the building). Other inputs to the system can beweather information (W(t)) and/or feedback from other energy assets inthe system (V). This model can be used, e.g., for co-optimization of anenergy storage asset and an energy consuming asset for the energymarket.

In an example according to a principle herein, once an appropriate assetmodel is established for a given energy asset or group of energy assets,different candidate operating schedules may be applied to the model tosimulate how the energy profile EP(t) of the asset(s) is affected as afunction of time, over a given time period T, by the different operatingschedules.

An example technique for facilitating determination of optimal operatingschedule for energy cost reduction and/or revenue generation fromwholesale electricity markets according to various examples disclosedherein is as follows. In this example, the system includes an energyconsuming asset, a controller of the energy storage asset, and acontrollable energy consuming asset. A plurality of first candidateoperating schedules is selected for the controller, and a plurality ofsecond candidate operating schedules is selected for the energyconsuming asset. Each second candidate operating schedule for the energyconsuming asset is different from the BAU operating schedule for theenergy consuming asset. The plurality of first and second candidateoperating schedules are successively applied to the mathematical modelto generate corresponding plurality of simulated energy profiles for theenergy storage asset and the energy consuming asset. A plurality ofprojected net energy-related costs to the energy customer are computed,where each projected net energy-related cost is computed based at leastin part on the representative CBL energy profile and the simulatedenergy profiles corresponding to the respective first and secondcandidate operating schedules and the forecast wholesale electricityprice. Respective ones of the first and second candidate operatingschedules corresponding to one simulated energy profile of the pluralityof simulated energy profiles that results in a minimum netenergy-related cost of the plurality of net energy-related costscalculated are selected as an optimal first operating schedule and anoptimal second operating schedule. That is, namely, this technique canbe implemented to simulate how energy assets consume/generateelectricity based on different candidate operating schedules for theasset(s), and to select a particular operating schedule that facilitatesa particular economic goal of the energy customer.

In another example, the operating schedules for the energy storage assetand energy consuming asset can be calculated in tandem based onminimizing the net energy-related costs (NEC), as discussed in greaterdetail below.

Operating Schedules and Constraints

In considering various operating schedules SP(t) that may be applied tothe asset model so as to simulate a corresponding energy profile EP(t),in some instances SP(t) may not be varied freely. Such limitations oncandidate operating schedules may be due at least in part to physicallimitations of the asset(s) being modeled, and/or limitations onoperation of the asset(s) dictated by the energy customer itself. Forexample, in some instances the customer may want to constrain the rangein which the magnitude of SP(t) may be varied at any given time, and/orthe customer may wish to designate particular periods of time (e.g.,within the given time period T of interest) during which particularvalues of SP(t) cannot be changed (or only changed in a limited manner).

For purposes of illustration, again consider a building asset with anHVAC system. The customer may specify that, in considering candidateoperating schedules SP(t) for the building asset, temperature set points(i.e., the magnitude of SP(t) in this example) must remain in a range offrom between 65 to 75 degrees F. in any proposed operating schedule;furthermore, the customer may dictate that during a certain time frame,the temperature set point may not exceed 70 degrees F. In general,magnitude and/or timing limitations placed on a candidate operatingschedule SP(t) for one or more modeled assets are referred to herein as“constraints” on the operating schedule.

The concept of candidate operating schedules for one or more modeledenergy assets subject to one or more “constraints” is denoted herein as:SP(t)|_(Constraints)≡operating schedule for one or more energy assetssubject to constraints

In an example, the system includes an energy storage asset, andconstraint may be placed on the allowed state of charge (SOC) of theenergy storage asset. For example, the constraint may be placed that theSOC does should not be allowed to fall below a minimal SOC value (i.e.,not too depleted) and/or that the SOC does should not be allowed to goabove a maximal SOC (i.e., not overly-charged).

Business-As-Usual (BAU) Conditions and Customer Baseline (CBL) EnergyProfiles

Once an appropriate asset model is established for a given energy assetor group of energy assets, a particular operating schedule of interestin some examples is referred to herein as a “typical” or“business-as-usual” (BAU) operating schedule (also referred to herein as“BAU conditions”), denoted as SP(t)_(BAU). In particular, “BAUconditions” refer to an operating schedule that an energy customer wouldtypically adopt for its energy asset(s), absent the incentive to reduceenergy costs and/or earn energy-related revenue from wholesaleelectricity markets. Again turning to the example of a building assetfor purposes of illustration, absent any incentive to change itsbehavior, during a summer season in which cooling is desired an energycustomer may typically set the thermostat (i.e., temperature set points)for the building asset at 72 degrees F. from 9 PM to 9 AM, and at 68degrees F. from 9 AM to 9 PM; this can be represented conceptually usingthe notation adopted herein as:

${{SP}(t)}_{BAU} = {\begin{Bmatrix}{72,} & {{9\mspace{14mu}{PM}} < t < {9\mspace{14mu}{AM}}} \\{68,} & {{9\mspace{14mu}{AM}} < t < {9\mspace{14mu}{PM}}}\end{Bmatrix}.}$

When a typical operating schedule SP(t)_(BAU) is applied to the assetmodel, the particular energy profile generated by the model is a specialcase referred to herein as a simulated “customer baseline” (CBL) energyprofile, denoted as CBL(t). Using the example relationship given in Eq.2 above (which includes consideration of weather information), thespecial case of a CBL energy profile may be conceptually representedmathematically as:F(SP(t)_(BAU) ,W(t))=CBL(t),  Eq. 6where the typical operating schedule SP(t)_(BAU) is an argument of thefunction F (in this example together with the weather information W(t)),and the CBL energy profile of the modeled asset(s) as a function of timeis denoted as CBL(t).

Although consideration of weather information W(t) is included in theexample above, it should be appreciated that the simulation of acustomer baseline (CBL) energy profile in other examples may notconsider weather information (as such information may not be relevant tothe energy profile of the asset(s) in question). It should also beappreciated that while the simulation of a CBL energy profile may beuseful for mathematical optimization techniques employed in someexamples to facilitate energy cost reduction and/or revenue generationfrom particular wholesale electricity markets (e.g., economic demandresponse “energy markets”), simulation of a CBL energy profile may notbe applicable or necessary in other examples to facilitate energy costreduction and/or revenue generation from wholesale electricity markets.

Objective Cost Functions and Optimal Control

For purposes of the present disclosure, an “objective cost function”specifies all energy-related costs and energy-related revenuesassociated with operating one or more modeled energy assets of an energycustomer so as to achieve a particular economic goal (an economic“objective”). In one aspect, an objective cost function incorporates thefunction(s) F representing the mathematical model for one or more energyassets, and specifies an energy customer's “net energy-related cost”(e.g., in dollars) associated with operating the modeled asset(s) over agiven time period T. The energy customer's net energy-related cost asgiven by the objective cost function is denoted herein as NEC$:NEC$=net energy-related cost to operate one or more energy assets.

As discussed in greater detail below, objective cost functions providinga net energy-related cost NEC$ according to different examples may havea variety of respective cost and revenue terms, based at least in parton the types of asset(s) being operated and the particularrevenue-generation objective(s) (e.g., the particular wholesaleelectricity market(s) from which revenue is being sought).

For example, in some examples, the energy-related costs included in theobjective cost function may include “actual” energy-related costs (e.g.,retail electricity costs, wholesale electricity costs representingrevenue earned by the energy customer, etc.). In some examples, theenergy-related costs included in the objective cost functionadditionally or alternatively may include “indirect” energy-relatedcosts, such as convenience/comfort costs associated with the energycustomer's adoption of a suggested operating schedule different than theBAU operating schedule (the convenience/comfort cost represents an“indirect” cost associated with a change in the customer's behavior withrespect to operating its asset(s), based on the incentive of possibleenergy-related revenue from the wholesale electricity markets).Similarly, an objective cost function may include one or more termsspecifying energy-related revenues corresponding to one or morewholesale electricity markets (e.g., “energy markets,” “synchronizedreserve,” “regulation”).

To provide a preliminary illustration of concepts germane to an objectcost function specifying a net energy-related cost NEC$, an examplerelating to economic demand response revenue from the wholesaleelectricity “energy markets” is first considered. To this end, retailelectricity prices (i.e., what the energy customer pays a “utility” forelectricity usage) and wholesale electricity-related product pricesavailable to the energy customer respectively are denoted as:Retail$(t)=price of electricity from a retail electricity provider(“utility”); andWholesale$(t)=price of electricity-related product on applicablewholesale electricity market,where the retail electricity price Retail$(t) and the wholesaleelectricity-related product price Wholesale$(t) may vary independentlyof each other as a function of time. In an example, the units of theretail electricity price Retail$(t) and the wholesaleelectricity-related product price Wholesale$(t) are $/MWh.

The wholesale price Wholesale$(t) can be dictated by (e.g., based atleast in part on) the “locational marginal price” (LMP) as a function oftime, as noted above (see Background section). However, depending on agiven wholesale electricity market and/or a particularelectricity-related product in question, it should be appreciated thatthe wholesale price Wholesale$(t) may be based on other and/oradditional factors. Also, practically speaking, wholesale prices are notcontinuous functions of time; rather, as discussed above, wholesaleprices based on the LMP may be calculated periodically at specifiednodes of the grid (e.g., every 5 minutes, every half-hour, every hour)depending on the particular market in which the energy customer isparticipating. Accordingly, it should be appreciated that Wholesale$(t)typically is a discrete function of time, with t having some periodicity(e.g., 5 minutes, 30 minutes, 60 minutes).

Given the notation above for retail and wholesale prices, the energycustomer's modeled retail electricity costs (or “supply costs”), foroperating one or more modeled electricity-consuming assets pursuant to aparticular operating schedule SP(t) applied to an asset model, isdenoted herein as Supply$(t), given by:Supply$(t)=EP(t)*Retail$(t),  Eq. 7wherein EP(t) is the energy profile of the modeled asset(s) (e.g., givenby any of Eqs. 1-4 above).

For the energy storage asset, the energy customer's “supply costs” forcharging the asset can be denoted herein as Supply$(t)_(ES), given by:Supply$(t)_(ES) =EP(t)*Retail$(t),  Eq. 8wherein EP(t) is the energy profile of the modeled energy storageasset(s). Since the energy profile for an energy storage asset can berepresented based on a charge rate (C_(t)) for a time step (t<T) overthe amount of time of charging (Δt), the supply costs can be expressedas:Supply$(t)_(ES) =C _(t) *Δt*Retail$(t).  Eq. 9The charge rate (C_(t)) may be the maximum charge rate of the energystorage asset, or a charge rate less than the maximum charge rate. Forexample, in different examples herein, the output of the controller maymodify the charge rate of the energy storage asset to values that areless than the maximum charge rate.

If the system includes an energy storage asset and an energy generatingasset, the total supply costs can be expressed, in a non-limitingexample, as the energy storage asset (Supply$(t)_(ES)) reduced by a costamount based on the amount of energy provided by the energy generatingasset (EG_(k)). In an example, the total supply costs can be expressedas:Supply$(t)_(total)=(C _(k) −EG _(k))*Δt*Retail$(t).  Eq. 10

Supply costs may also apply to the system by virtue of the reduction inlife of the energy storage asset. An energy storage asset may have alimited life depending on its rating of expected charge/dischargecycles. A portion of the costs associated with ultimately replacing anenergy storage asset at the end of its lifetime may be included in thesupply costs based on the number of charge/discharge cycles it isexpected to undergo when implemented in an energy market and/or aregulation market as described herein. The lifetime reduction supplycosts may also depend on the number of kWh is used in each charge ordischarge cycle, and/or for what length of time the energy storage assetis used in a market (energy, regulation, etc.). For example, thecontribution to the supply costs based on the replacement cost(Replacement$) may be computed according to the expression:Supply$(t)_(LIFE)=Replacement$/n  Eq. 11where n represents an effective number of charge/discharge cycles. Theeffective number of charge/discharge cycles can depend on the number ofcycles the asset is expected to undergo when implemented in an energymarket and/or a regulation market, the number of kWh is used in eachcharge or discharge cycle, and/or for what length of time the energystorage asset is used in a given market. This lifetime supply cost wouldbe additive to any of the expressions for supply costs described hereinfor a system that includes an energy storage asset.

With respect to economic demand response revenue from the wholesaleelectricity energy markets, in the present example it is presumed thatthe energy customer is amenable to operating its energy asset(s)pursuant to a candidate operating schedule that is different than its“typical operating schedule” or BAU conditions (i.e., SP(t)_(BAU)), suchthat the energy profile EP(t) of the asset(s) will be on average lowerthan the customer baseline CBL(t) (see Eq. 6 and related descriptionabove). Altering the energy profile of the asset(s) with respect to thecustomer baseline, pursuant to a change in behavior represented by acandidate operating schedule different than BAU conditions, provides thesource of opportunity for generating economic demand response revenuefrom the wholesale electricity energy markets. Accordingly, a wholesaleelectricity energy market “demand response revenue,” denoted herein asDR$(t)_(EM), is given generally by:DR$(t)_(EM)=max{0,[(CBL(t)−EP(t))*Wholesale$(t)]}.  Eq. 12

For an energy storage asset in an energy market, a demand responserevenue may be denoted herein as DR$(t)_(ES), is given generally by:DR$(t)_(ES)=(0−(−(D _(t)))*Δt*Wholesale$(t).  Eq. 13

As described herein, a system that includes an energy storage asset canparticipate in both an energy market (at a price of Wholesale$(t)) andin a regulation market (at a price of regulation$(t)). In this example,the demand response revenue may be computed herein as DR$(t)_(ES),denoted by:DR$(t)_(ES)=(εD _(t))*Δt*Wholesale$(t)+(γD _(t))*Δt*regulation$(t)  Eq.14where D_(t) denotes the discharge rate of the energy storage asset at atime step. Where the system participates in the energy market and theregulation market at different points in time during overall time periodT, both multipliers of the discharge rate, ε and γ, may be equal to 1.In different examples herein, the output of the controller may modifythe discharge rate of the energy storage asset to values that are lessthan the maximum discharge rate. Using the principles of virtualpartitioning described herein, by apportioning an output of thecontroller in communication with the energy storage asset, a portion ofthe discharge rate may be directed to the regulation market and anotherportion directed to the energy market during a given time step. As anon-limiting example, the operating schedule determined as describedherein may cause the controller to discharge the energy storage asset ata discharge rate of εD_(t) to the energy market, while concurrentlyrespond to the regulation market at a discharge rate of γD_(t) alongshorter timescales (such as but not limited to at 2-second intervals orminute-by-minute time intervals). Here, the constraint on the values maybe ε+γ≦1 if D_(t) represents the maximum discharge rate of the energystorage asset.

In a non-limiting example, where the regulation price is not based onthe discharge rate, but rather depends only on the time period ofcommitment of the energy storage asset to the regulation market, thedemand response revenue may be computed as:DR$(t)_(ES)=(εD _(t))*Δt*Wholesale$(t)+regulation$(t)*Δt  Eq. 15

In another example, the demand response revenue for a system thatincludes an energy storage asset and an energy generating assetparticipating in an energy market may be computed as:DR$(t)_(ES+EG)=(D _(t))*Δt*Wholesale$(t)+(E _(EG))*Wholesale$(t)  Eq. 16where D_(t) denotes the discharge rate of the energy storage asset at atime step and E_(EG) denotes the energy provided by the energygenerating asset.

According to the principles described herein, a demand response may alsobe generated for a system that includes an energy storage asset and anenergy generating asset participating in both an energy market and aregulation market.

Based on the equations for supply costs and demand response above, anexample of an objective cost function to provide a net energy-relatedcost NEC$ over a given time period T for operating the modeled asset(s),considering both retail electricity supply costs and demand responserevenue can be computed based on the expression:

$\begin{matrix}{{{NEC}\;\$} = {\sum\limits_{t}^{T}\;{\left( {{{{Supply}\$}(t)} - {{DR}\;{\$(t)}}} \right).}}} & {{Eq}.\mspace{14mu} 17}\end{matrix}$

In one example, an objective cost function as exemplified by Eq. 17 maybe provided to an optimizer (a particularly-programmed processor, alsoreferred to as a “solver”; such as processor unit 13 of FIG. 2) thatimplements a mathematical optimization process to determine a suggestedoperating schedule for the energy asset(s) over the time period T thatminimizes the net energy-related cost NEC$. Accordingly, the optimizersolves for:

$\begin{matrix}{{Min}\left\lbrack {\sum\limits_{t}^{T}\;\left( {{{{Supply}\$}(t)} - {{DR}\;{\$(t)}}} \right)} \right\rbrack} & {{Eq}.\mspace{14mu} 18}\end{matrix}$

By substituting the pertinent equations for supply costs and demandresponse (which depends on the energy assets in a given system) backinto Eq. 18, the various informational inputs provided to the optimizermay be readily ascertained.

As a non-limiting example, for a system that is participating in theenergy market, the various informational inputs provided to theoptimizer may be readily ascertained as follows:

$\begin{matrix}{{{Min}\left\lbrack {\sum\limits_{t}^{T}\;\left\{ {\left( {{{EP}(t)}*{{{Retail}\$}(t)}} \right) - \left( {\max\left\{ {0,\left\lbrack {\left( {{{CBL}(t)} - {{EP}(t)}} \right)*{{{Wholesale}\$}(t)}} \right\rbrack} \right\}} \right)} \right\}} \right\rbrack},} & {{Eq}.\mspace{14mu} 19}\end{matrix}$where from Eq. 2EP(t)=F(SP(t)|_(Constraints) ,W(t)),and from Eq. 6CBL(t)=F(SP(t)_(BAU) ,W(t)),where again it is presumed for purposes of illustration that weatherinformation W(t) is relevant in the present example. From the foregoing,it may be seen that one or more of the following inputs may be providedto the optimizer in various examples:

-   -   F—one or more functions defining the mathematical model for the        energy asset(s);    -   SP(t)_(BAU)—BAU or “typical” operating schedule for the energy        asset(s);    -   Constraints—any timing and/or magnitude constraints placed on        candidate operating schedules for the energy asset(s);    -   W(t)—weather information as a function of time (if appropriate        given the type of energy asset(s) being operated);    -   u(t)—control vector for the controller in communication with the        energy storage asset;    -   Retail$(t)—retail price of electricity as a function of time;    -   Wholesale$(t)—wholesale price of electricity-related product as        a function of time;    -   Regulation$(t)—regulation price in regulation market as a        function of time; and    -   NEC$—the objective cost function describing the energy        customer's net energy-related cost associated with operating the        modeled energy asset(s).

Based on the foregoing inputs, the optimizer solves Eq. 19 by finding an“optimal” operating schedule for the energy asset(s), denoted herein asSP(t)_(opt), that minimizes the net energy-related cost NEC$ to theenergy customer:SP(t)_(opt)=“optimal” or suggested operating schedule for one or moreenergy assets

In various implementations described herein, the optimizer may receiveone or more inputs, including but not limited to, the weatherinformation W(t), the retail electricity price Retail$(t), and thewholesale price of the electricity-related product Wholesale$(t) (andthe regulation price (regulation$(t))) as forecasted values providedfrom a third-party source, for the time period T over which theoptimization is being performed.

While a given optimizer in a particular implementation may employvarious proprietary techniques to solve for the minimization of anobjective cost function according to various examples of the principlesherein, conceptually the optimization process may be generallyunderstood as follows. In various implementations discussed herein, theoptimizer generates the operating schedule using the model of the systemthrough an optimal control procedure. In the various exampleimplementations, the optimizer determines an optimal operating scheduleover the defined time period (T) by optimizing an objective costfunction. For example, the optimizer can be implemented to determine theoperating schedule that generates the energy-related revenue byminimizing a function representing the net energy-related costs of thesystem over the time period (T). The net energy-related costs can becomputed based on the supply costs and the demand response revenue asdescribed herein, including in Eqts. 1-19 above. The optimizer optimizesthe objective cost function over the entire defined time period (T) togenerate the operating schedule. The generated operating schedule caninclude suggestions, for different specific time intervals within theoverall time period T, for when the controller can be used to implementthe energy storage asset in the energy market, in the regulation market,or in both the energy market and regulation market (through dynamicpartitioning).

In a non-limiting example of an implementation of the optimizer, somenumber N of candidate operating schedules SP(t)|_(Constraints) for themodeled asset(s) (together with weather information W(t), if appropriatebased on a given objective function) can be successively applied to theasset model given by the function(s) F to generate simulated energyprofiles EP(t) corresponding to the candidate operating schedules (seeEqs. 1-4). A net energy-related cost NEC$ given by the objective costfunction is calculated for each such simulated energy profile EP(t) (seeEq. 17), and the candidate operating schedule that minimizes theobjective cost function (i.e., the “optimal” operating scheduleSP(t)_(opt) that minimizes the net energy-related cost NEC$) is selectedas the suggested operating schedule to be provided to the energycustomer.

As noted earlier, the example above in connection with the objectivecost function of Eq. 17 is based on actual energy-related costs (e.g.,retail electricity cost) Supply$(t). In other examples, theenergy-related costs included in a given objective cost functionadditionally or alternatively may include “indirect” energy-relatedcosts, such as “convenience/comfort” costs associated with the energycustomer's adoption of a suggested operating schedule SP(t)_(opt)different than its typical operating schedule SP(t)_(BAU). In one aspectof such examples, a convenience/comfort cost represents an “indirect”cost in that it does not necessarily relate to actual energy-relatedexpenditures, but rather attributes some cost (e.g., in dollars)relating to a change in the customer's behavior with respect tooperating its asset(s), based on the incentive of possibleenergy-related revenue from the wholesale electricity markets.

Accordingly, in some examples, an alternative objective cost functionsimilar to that shown in Eq. 17 may be given as:

$\begin{matrix}{{{{NEC}\;\$} = {\sum\limits_{t}^{T}\;\left( {{{{Comfort}\$}(t)} + {{{Supply}\$}(t)} - {{DR}\;{\$(t)}}} \right)}},} & {{Eq}.\mspace{14mu} 20}\end{matrix}$where Comfort$(t) represents a convenience/comfort cost associated witha change in the energy customer's behavior with respect to operating itsasset(s).

A convenience/comfort cost Comfort$(t) may be defined in any of avariety of manners according to different examples. For example, in oneimplementation, a convenience/comfort cost may be based at least in parton a difference (e.g., a “mathematical distance”) between a givencandidate operating schedule and the typical operating schedule (BAUconditions) for the modeled asset(s)—e.g., the greater the differencebetween the candidate operating schedule and the typical operatingschedule, the higher the convenience/comfort cost (there may be moreinconvenience/discomfort attributed to adopting a “larger” change inbehavior). This may be conceptually represented by:Comfort$(t)=G[|SP(t)|_(Constraints) −SP(t)_(BAU)|],  Eq. 21where G specifies some function of the absolute value of the“difference” between a candidate operating schedule (e.g., in a giveniteration of the optimization implemented by the optimizer) and thetypical operating schedule.

To provide an example of how Eqs. 20 and 21 may be employed in anoptimization process to determine a suggested operating scheduleSP(t)_(opt) for an energy customer according to one example, againconsider a building asset operated by the energy customer, for which agiven operating schedule SP(t) is constituted by a temperature set pointas a function of time. If T(t)_(BAU) represents the temperature setpoints constituting a typical operating schedule, andT(t)|_(Constraints) represents different temperature set pointsconstituting a candidate operating schedule that may be adopted tofacilitate energy-cost reduction and/or revenue generation, theconvenience/comfort cost Comfort$(t) in this example may be defined as a“temperature set point deviation” T_(dev)(t), according to:Comfort$(t)≡T _(dev)(t)=A(|T(t)|_(Constraints) −T(t)_(BAU)|),  Eq. 22where A is a constant that converts temperature units to cost units(e.g., degrees F. to dollars). Eq. 22 specifies that there is a greater“indirect” cost associated with candidate operating schedules havingtemperature set points that deviate more significantly from the typicaltemperature set points (albeit within the constraints provided by theenergy customer). In this manner, as part of the optimization process,potential revenue from the wholesale electricity markets may be“tempered” to some extent by a perceived cost, included in the objectivecost function (see Eq. 20), that is associated with theinconvenience/discomfort of deviating significantly from the typicaloperating schedule.

In the example above, although the multiplier A in Eq. 22 is discussedas a conversion constant, it should be appreciated that in otherexamples A may be an arbitrary function having as an argument theabsolute value of the difference between a candidate operating scheduleand the typical operating schedule as a function of time. Moregenerally, it should be appreciated that a convenience/comfort costComfort$(t) is not limited to the “temperature-related” example providedabove in connection with a building asset, and that other formulationsof a convenience/comfort cost as part of an objective function arepossible according to various examples of the principles herein.

In yet other examples of objective cost functions, different cost andrevenue terms of a given objective cost function may includecorresponding “weighting factors” (e.g., specified by the energycustomer), so as to ascribe a relative importance to the energy customerof the respective terms of the objective cost function in arriving at asuggested operating schedule SP(t)_(opt). For example, in someinstances, an energy customer may want to emphasize the importance ofincreasing prospective demand response revenue DR$(t) vis a visdecreasing supply costs Supply$(t) in solving the optimization problemto arrive at a suggested operating schedule; similarly, in otherinstances, an energy customer may want to emphasize convenience/comfortcosts Comfort$(t) vis a vis increasing prospective demand responserevenue DR$(t) in solving the optimization problem to arrive at asuggested operating schedule. The ability of an energy customer totailor a given objective cost function according to weighting factorsfor respective terms of the objective cost function provides an“elasticity” to the optimization process. Using the objective costfunction given in Eq. 20 above as an example, in one example suchweighting factors may be included in the specification of an objectivecost function as respective term multipliers:

$\begin{matrix}{{{{NEC}\;\$} = {\sum\limits_{t}^{T}\;\left\lbrack {\left( {\alpha*{{{Comfort}\$}(t)}} \right) + \left( {\beta*{{{Supply}\$}(t)}} \right) - \left( {\gamma*{DR}\;{\$(t)}} \right)} \right\rbrack}},} & {{Eq}.\mspace{14mu} 23}\end{matrix}$where α, β, and γ constitute the weighting factors, and (α+β+γ=1).

FIG. 11 shows a non-limiting example of a implementation of an energystorage asset based on an operating schedule generated through applyingan optimization, through optimal control, and using a net-energy relatedcost function based on a model of the system state function. The systemincludes the energy storage asset and a controller. The plot shows theprojected LMP prices over the period of the optimization (T=24 hours,divided into 48 half-hour time intervals), the state of charge of theenergy storage asset, the periods of charging and periods of dischargingof the energy storage asset (where the height of the bar represents theamount/degree of the charging or discharging). In response to theoperating schedule, the initial period of charging the energy storageasset occurs during a period of low LMP prices. The optimization basedon the optimal control determines that the time intervals for charge anddischarging during the period when LMP prices are higher is optimal forproviding overall energy-related revenue to the customer over the entiretime period T.

In an example implementation, the operating schedule can be generatedthrough applying an optimization using a net-energy related costfunction based only on the energy market. The result of the optimizationcan be used to provide recommendation for time intervals for the energycustomer to participate in the regulation market. For example, based onthe results of the optimization in FIG. 11, the operating schedule maydetermine that any excess charge/discharge capacity of the controller ofthe energy storage system may be committed to the regulation market onan hour-by-hour basis. For example, based on the results of FIG. 11, itcan be determined that the any excess charge/discharge capacity of thecontroller may be committed to the regulation market during the first 15time intervals. The optimization may make such a determination dependingon whether the forecast regulation price in the regulation market inthis time interval offers opportunity for energy-related revenue duringthis time interval or if considered in the context of the globaloptimization over time period T. In an example, such a determination maybe made depending on whether the SOC of the energy storage asset isfeasible for its use in the regulation market. For example, it may bepreferable for the energy storage asset to be near around a 50% SOC forit to be applicable to the regulation market. In addition, if it isdecided to commit the energy storage asset to the regulation market fora time interval, e.g., for one or more 1-hour time intervals, theoptimization described herein may be re-performed based on the new inputstate of the system. Such new inputs can include the state of charge ofthe energy storage asset after its commitment to the regulation marketends. In another non-limiting example, the optimization may evaluatedifferent SOC initial inputs to assess whether “recovery” from theregulation market is feasible for later participation in the energymarket.

In an example, a predetermined threshold value of wholesale electricityprice can be set at which it is decided that the excess charge/dischargecapacity of the controller will be committed to the regulation market.Based on the results of the optimization in FIG. 11, a predeterminedthreshold value of the LMP price, indicated by the dashed horizontalline, may be set. In addition, it may be determined that the first timeinterval of charging the energy storage asset occurs during the timeperiod that T coincides with the time interval during which the forecastwholesale electricity price falls below the predetermined thresholdvalue. It may also be determined in the operating schedule that a secondtime interval of discharging the energy storage asset occurs coincideswith a time interval during which the forecast wholesale electricityprice exceed the predetermined threshold value (such as during intervals26 to 36 in FIG. 11).

While the discussion above of exemplary objective cost functions andoptimization of same to generate suggested operating schedules forenergy assets has been based at least in part on economic demandresponse revenue from wholesale electricity energy markets (and in someparticular examples involving building assets), it should be appreciatedthat the disclosure is not limited in this respect; namely, according toother examples, objective cost functions may be formulated and optimizedto achieve a wide variety of energy-related objectives associated withdifferent types of energy assets and revenue generation opportunitiesfrom wholesale electricity markets. For example, computation based onrevenue from the regulation market has also been described herein above,and optimization based on the wholesale price and the regulation priceare described herein below. In other examples, the principles herein canbe applied to other markets, such as the spinning reserve market.

Generating an Operating Schedule for Deriving Energy-Related Revenue

As discussed above, the output of an optimization process to minimize anenergy customer's net energy-related cost NEC$ (e.g., as specified by anobjective cost function) is typically provided as a suggested operatingschedule SP(t)_(opt) for one or more energy assets. Generally speaking,the suggested operating schedule SP(t)_(opt) may comprise one or moreset point values as a function of time that take into consideration allof the energy customer's modeled and controllable energy assets.

For example, in some instances involving multiple individually modeledand controllable energy assets, the suggested operating scheduleSP(t)_(opt) may comprise multiple time-varying control signalsrespectively provided to corresponding controllers for the differentenergy assets. In other cases, the energy customer may have an energymanagement system (EMS) that oversees control of multiple energy assets,and the suggested operating schedule SP(t)_(opt) may comprise a singlecontrol signal provided to the energy customer's EMS, which EMS in turnprocesses/interprets the single control signal representing thesuggested operating schedule SP(t)_(opt) to control respective energyassets.

In examples in which the energy customer normally operates its energyasset(s) according to a typical operating schedule SP(t)_(BAU) (absentany economic incentive to change its energy-related behavior), thesuggested operating schedule SP(t)_(opt) may be conveyed to the energycustomer in the form of one or more “bias signals,” denoted herein byBias(t). In particular, one or more bias signals Bias(t) may represent adifference between the suggested operating schedule and the typicaloperating schedule as a function of time, according to:Bias(t)=SP(t)_(opt) −SP(t)_(BAU).  Eq. 24

Dynamic Virtualization

Dynamic virtualization is an integrated solution for energy generationand storage involving energy assets, such as batteries and solargenerators. This uses a version of examples with virtual partitioning ofan energy storage device. Dynamic virtualization can be used toco-optimize energy storage assets and solar generation across differentenergy markets or other uses. These markets or uses may include (1)electric energy provided over the grid to the energy market, and (2) theancillary services market (which may include regulation, which isfocused on regulation of power frequency and voltage on the grid) or (3)use of the storage device to maintain power quality at the owners'facilities.

Dynamic virtualization uses examples of systems with the virtualpartitioning of the battery or other type of energy storage asset intovirtual separate batteries, each virtual energy storage asset beingallocated to separate markets or functions, such as participating in theenergy market, and the ancillary services (regulation) market or use tomaintain power quality at the premise. The virtual partition of thebatteries is not physical, but is instead an allocation of energystorage asset capacity to various markets or uses. This virtualpartition by allocation is dynamic in that it can be constantly changedin response to changing price points and performance requirements duringthe day.

There are rapid swings in load on the spot electric energy market. Inorder to maintain electrical balance on the grid and regulate consistentpower and voltage on the grid over short periods of time, for example,over periods of four seconds, fifteen seconds, or one minute, the gridoperator sends out signals to change generation to match the loadchanges. Batteries are particularly well suited to respond to theseshort response time signals.

With examples of the principles herein, energy storage assets such asbatteries can be applied to swing between the markets for energy andancillary services for regulation of the grid or for the maintenance ofpower quality at the energy storage asset owner's facility. In the past,batteries were not purchased and installed for the purpose of providingregulation services, because batteries tend to be too expensive for thispurpose alone. Most regulation services now come from gas poweredgenerators providing about 1-10 megawatts, and these energy assets taketime to turn on and off. Industrial batteries, however, are instant onand off and usually provide power in the 1 megawatt range—and canrespond to grid operator signals in milliseconds.

In the past, energy storage and energy storage asset facilities wereusually purchased with the intent to provide backup power for theowners, in case the electric power grid goes down or temporarilyprovides inadequate power. However, once the battery or other type ofenergy storage assets are installed to satisfy backup capacity for theowner, they may also to some extent be active in the regulation marketto regulate the power and voltage on the grid, and in the energy market,to sell power into the grid in response to real-time pricing changes (orto cut the user's demand on the grid). For example, energy storageassets may discharge to the grid during high LMP price hours.

Energy storage assets may include batteries, ice units, compressed air,or other technologies to store energy on site by users and generators ofpower. Batteries may be of any type, including lithium ion, lead acid,flow batteries, dry cell batteries, or otherwise.

Solar generators of power may include solar panels, solar cells, anyother photovoltaic power generator, or any means for generating powerfrom sunlight. This may also include generation of electricity fromsteam or similar use of liquid to gas phase generation from sunlight, togenerate electricity.

The energy market involves generating power, distributing power into thegrid, and drawing power out of the grid, each at a price. This ismeasured in terms of megawatt hours that are the amount of powerdelivered. Energy is delivered for sustained periods of time, such asfor 15 minutes or more.

The capacity market is measured in terms of megawatts of capacity. Inthis market, a seller makes their facilities available to generateelectricity when needed and holds them in reserve for that purpose, butmay never actually distribute energy into the grid rather than just beon-call. This, in effect, pays the seller to be available and impactsthe reliability of the grid.

The ancillary market includes regulation of frequency and voltage in thegrid, and the provision of an operating reserve. The regulation of thevoltage in the grid involves discharging energy into the grid orabsorbing energy from the grid in small increments, frequently, forshort periods of time, and very rapidly.

Smart grid services increasingly rely on new technologies such asrenewable energy and large-scale storage resources. Unfortunately, thelife-cycle costs associated with such resources, when takenindividually, are still high compared with more traditional forms ofenergy production. In addition, the desired proliferation of distributedand renewable resources on the power grid introduces new threats to itsreliable operation, as they are subject to unpredictable drops inoutput, such as when the wind stops blowing. Consequently, both economicand reliability issues introduce substantial obstacles to a highpenetration of those technologies in the power grid.

By themselves, storage resources such as electrical batteries arepresently high cost options. Likewise, photovoltaic generation and windturbines are comparatively quite expensive and their intermittencycreates new strains on the power grid.

However, when optimally managed by various examples disclosed herein toprovide timely support to the power grid, the net cost of electricalstorage can be substantially reduced, as the result of payments by thegrid operator (ISO/RTO) provides for facilities that can be called on toprovide such support. Also, combining energy storage with intermittentgeneration makes technologies such as wind and solar more predictable onthe grid, and hence, more valuable.

Examples, including dynamic virtualization, can dramatically improve theeconomics of renewable generation and storage technologies, byco-optimizing their operation to participate in the various energy andancillary services (including regulation) markets and thus maximizetheir economic benefits.

Examples focus on the economics of batteries and energy storage and, byproviding energy resource optimization and a gateway to the wholesalemarkets, can help facility managers deploy a comprehensive energystorage solution that can cost-effectively meet an organization'sbusiness objectives.

More broadly, when optimally coupling energy storage with renewablegeneration, various examples redefine the economics of such resources,while providing firm, dispatchable virtual generation that supports thereliability objectives of the power grid. Thus, by integratingdistributed resources into virtual generation via system operatordispatch, examples can help enable the acceleration of renewable energygeneration technologies such as solar and wind.

Systems Including Energy Storage Assets

Large-scale storage is widely seen as a necessary piece of the smartgrid and a key component of America's electricity future. Thisrecognition is driven by the following factors: (1) the growing adoptionof intermittent renewable power sources; (2) state and nationwide budgetshortfalls, leading local governments to seek cost-effective solutionsfor maintaining America's aging infrastructure; and (3) the widespreadbelief that electric vehicles (“EVs”) will materially grow their marketshare over the next 5 to 15 years.

In this context, stakeholders have been looking for ways to acceleratethe development and implementation of grid-level storage. Effectivebattery and other energy storage asset solutions can take unpredictableenergy resources and turn them into reliable power, while matchingelectricity supply to demand; they play a crucial role in fosteringmicrogrids and distributed generation, viable alternatives to expandingthe U.S.'s power infrastructure; and they can address the new and uniqueconcerns created by EVs, such as helping to maintain grid stability andgiving utilities and grids more control over energy dispatch.

A key concern with batteries has long been their high upfront cost andlong payback periods. Various examples address this by providingbattery-owners a robust gateway to the wholesale electricity markets,thus unlocking new streams of revenues that increase their return oninvestment. This may also apply to other types of energy storage assets.

Various examples provide processor-executable instructions (includingsoftware solutions) that optimizes participation in wholesale markets byproviding energy storage asset owners with dynamic virtualization, aservice that continuously re-partitions the energy storage asset fordifferent markets and uses, chiefly real-time energy, and regulation,and power quality control, in an optimized manner, based on pricing andweather data, retail electricity rates, and characteristics of theenergy storage asset and its host site.

For large retailers and supermarkets, backup generation is a necessarybut often expensive proposition. The nation's largest big box chainshave taken a variety of approaches to minimizing the costs of providingsubstitute power in the case of an emergency or brownout; but for manystores, their only choice to date has been inefficient and costly dieselgenerators.

Examples with dynamic virtualization optimally manage a energy storageasset's state of charge based on the revenue producing opportunities inthe wholesale market, as well as the organization's business objectives,such as providing backup power to critical loads for a given period oftime. Thus, when paired with these examples, the energy storage assetbecomes an energy resource that will concurrently: (1) participate inthe energy markets by providing a way to shift the net load of afacility from high- to low-price periods; (2) participate in thefrequency regulation market by responding to real-time signals from thegrid operator; (3) participate in other wholesale markets, such asenergy and synchronized reserve; and (4) provide reactive/voltagesupport to the microgrid/distribution grid.

Examples enable the energy storage asset to maximize revenues from thevarious wholesale markets, while maintaining its ability to achieve itsmain objective of providing a reliability service to the organization.To achieve this, examples herein describe virtualization of the energystorage asset and creating dynamic “energy storage asset partitions,” ina manner similar to the way computing resources are virtualized. Throughits optimization capability, an example determines in hourly incrementswhich portion of the controller output (including its capacity), andhence the energy storage asset capacity (including its SOC), can beallocated to the energy and regulation markets respectively, whilemaintaining sufficient reserve to meet the forecasted backuprequirements. The optimal control (to perform the optimization describedherein) can take into account the forecasted and real-time hourly pricesfor each of the markets, along with the time and weather dependentbackup requirements of the facility. When combined with other resourcessuch as renewable generation, backup generation or demand response, theexamples described herein can extract the maximum value of all suchresources while meeting the organization's reliability, comfort, andsustainability objectives.

Following is a description of the different markets, including energymarkets and regulation markets, to illustrate how each market can affectthe operation of an energy storage asset.

Regulation Market

In a non-limiting example, capacity of the energy storage asset may becommitted to the regulation market to maintain the frequency and/orvoltage on the power line. For example, system operators seek tomaintain the system frequency at very near to a nominal frequency ofaround 60 Hz in the U.S. or around 50 Hz in some other countries(including countries in the European Union). If the frequency is toohigh, there is too much power being generated in relation to load. Asystem operator would send a signal to participants in the regulationmarket to increase their load, or ask for generation to be reduced, tokeep the system in balance. If the frequency is too low, then there istoo much load in the system, and the system operator would send a signalasking for generation to be increased or the load reduced. A gridoperator may use a real-time communication signal to call for either apositive correction (referred to in the industry as “regulation up”) ornegative correction (referred to as regulation down”). If load exceedsgeneration, the frequency and voltage tend to drop. The ISO/RTO systemoperator would relay a signal requesting regulation up. If, however,generation exceeds load, the frequency tends to increase. The ISO/RTOsystem operator would relay a signal requesting regulation down(including asking for reduced generation).

The regulation market may seek commitment of a system on an hourlybasis. However, the ISO/RTO system operator may relay regulation signalsfor regulation up and/or regulation down at much shorter timescales. Forexample, during the commitment period, the adjustments of regulation maytake place minute-by-minute, on the order of a minute or a few minutes,or on the order of a few seconds (e.g., at 2-second or 4-secondintervals). To participate in the regulation market, a resource mayreceive and may need to respond to a regulation signal generated by thegrid operator approximately every 2 seconds. (In some territories, thisrule may be relaxed somewhat for batteries.) The energy storage assetresponds to this signal with a percentage of its maximum resourcecapability that is bid into the regulation market. Examples receive andrespond to this signal and distribute it among the various resourcesparticipating in the regulation market within a given price zone, basedon the results produced by an optimizer.

If the ISO/RTO system operator sizes the regulation signals toadequately balance the signal in the long run, the charge of the energystorage asset may merely fluctuate around its initial state of chargewhen it started to provide regulation. That is, the proportion of theavailable state of charge of the energy storage asset that is committedfor use to provide regulation may be delivered at variable charge ratesor discharge rates. Adequately balanced regulation signals shouldneither completely deplete nor fill the energy storage asset.

In a non-limiting example, the regulation price may be set at averagevalues of around $30-$45/MW per hour, with hourly rates fluctuatingaround this average value. Some regulation markets may pay simply forthe commitment of an available capacity of the energy storage assetduring a time period, such as for an hour, with a separate payment forthe total amount of energy ultimately provided. Thus, payment at theregulation price may be made for the period of commitment, even if thesystem is not called upon to provide regulation during the commitmentperiod.

There may also be additional payment from the energy market for energygenerated, based on the wholesale electricity market price (the LMP).

Operating characteristics of the energy storage asset include power (orits instantaneous delivery capability in kW) and the energy stored inthe energy storage asset (or the amount of power it can generate overone hour, or kWh). In a non-limiting example, a battery rated at 1.5 MWpower and 1.0 MWh energy storage capacity will be able to provide 1.5 MWpower for a total period of 40 minutes (60×1/1.5). Thus, if the ownerbids 1.5 MW into the regulation market for a given hour, a 50% dischargesignal over 2 seconds could decrease the battery's charge level by 0.8kWh (1.5 MW×1/1800 hrs).

As part of a certification for participating in the regulation market,the ISO/RTO system operator may verify that the energy storage asset iscapable of responding to the regulation bid into the market. The ISO/RTOsystem operator may require that the energy storage asset be able to becharged/discharged at its full enrolled amount, when receiving a +/−100%regulation signal within a duration of 10 minutes. In the 1.5 MW exampleabove, the battery charge would be increased/decreased by +/−250 kWh(1.5 MW×1/6 hr).

For example, assuming that the energy storage asset starts with aninitial state of charge of 50% at time t=0. Ideally, the regulationsignal is “net zero,” meaning that the quantity of charged/dischargedenergy averages to zero over a given 24-hour period. In reality, thestate of charge of the energy storage asset may at times drift to thelimits of the energy storage asset's recommended state of charge. If thestate of charge exceeds some adjustable maximum or minimum values,various examples include compensating by exiting the regulation marketfor the next hour and bringing the energy storage asset back to itsinitial set-point.

In an example, the operating schedule that is generated according to animplementation of an apparatus herein specifies intervals of time whenthe energy storage asset may be committed to the regulation market.During these time periods, the operating schedule may additionallyindicate the points during these intervals of time where energy may bebought to charge the energy storage asset if its state of charge fallsbelow a desirable limit, or where excess energy may be sold if the stateof charge is too high. This discharge can contribute to a short-termdemand response action in the real-time energy market.

Energy Market

To participate in the energy market, the energy storage asset should tobe able to provide the “as bid” energy into the real-time market for thenext hour. Various examples compute the optimal charge or dischargesignal in anticipation of or in response to the economic signals, whilemaintaining minimum and maximum constraints on the state of charge ofthe energy storage asset. When combined with other controllableresources, such as renewable generation or advanced lighting and HVACsystems, examples extract the maximum economic value of each resource,given external factors and constraints. For example, examples can use anenergy storage resource to compensate for the intermittency of renewablegeneration, and can include demand response actions to help maintain thebalance.

FIG. 12 shows an example energy storage asset optimization in responseto economic signals and performance needs. The horizontal axis is timeover a 24 hour cycle. The left vertical axis is megawatt hours. Theright vertical axis shows price in dollars per megawatt hours. Thevolume under the line battery 810 shows the stored capacity in thebattery. The three lines below the horizontal axis shows the discharge820 from the battery. The seven vertical lines 830 above the horizontalaxis shows charging to the battery 830. The line 840 shows the LMPenergy price throughout the 24-hour cycle to which indicated energyassets are responding. In this example, examples determine the optimizedhourly charge and discharge schedule of a 1.5 MW/1.0 MWh battery inresponse to an LMP price signal. The optimization is further constrainedto maintain a 200 kWh minimum capacity for backup purposes, and amaximum capacity of 800 kWh to maintain charge/discharge cycleefficiency.

Spinning Reserve Market

To participate in the spinning reserve market, the energy storage assetshould to be able to commit resources to provide power during unplannedoutages of base load generators. Spinning reserve is generationcapability that can provide power to the grid immediately when calledupon by the ISO/RTO and reach full capacity within 10 minutes. Theenergy storage asset needs to be electrically synchronized with thegrid, e.g., through the controller, to participate in this market.Revenue in the spinning reserve market is for capacity rather thanenergy. It requires quick response but makes low total energy demand.Requests in the spinning reserve market may be made around 20-50 timesper year.

Revenue for the spinning reserve market may be determined based on theability of an energy storage asset to provide power during an unplannedevent, such as a generator failure. Revenue may also be derived based onthe amount of energy (MWh) that is generated during active participationin the spinning reserve market, such as based on the electricitywholesale price.

Co-Optimization Across Multiple Markets

As described above, the economic signal can be a driver for the averagecharge status of the energy storage asset. It responds to price signalsthat are averaged on an hourly basis. The regulation signal can be seenas having a “bias” effect over the average charge, in response to theregulation commands. Examples co-optimize the energy storage assetcharge by first economically optimizing the charge status of the energystorage asset, then allocating the balance of the available power to theregulation market, on an hourly basis.

By adding user-adjustable upper and lower constraints to the optimizedenergy storage asset charge, examples take into account reliabilityobjectives (e.g. backup) and charge/discharge cycle efficiency. Otherconstraints can be added, based on the type of energy storage assettechnology used, to maximize charge/discharge round trip efficiency, andoptimize energy storage asset life versus energy storage assetreplacement costs.

In addition to co-optimizing a storage resource at a given location,examples have the capability to perform a global optimization acrossmultiple customers within the same price zone, and disaggregate theregulation and economic signals among the various customers. Inparticular, this gives customers that do not have the minimum energystorage asset capacity required the ability to participate in theregulation market.

Co-Optimization with Other Distributed Resources

With various examples, distributed resources can earn maximum economicbenefit through co-optimization. Co-optimization of various resources onone site results in accelerated payback for all assets, and this, inturn, accelerates the market-wide penetration of these resources.

FIG. 13 shows an example generation schedule for battery-photovoltaicco-optimization. FIG. 13 shows an example where the same battery used inthe previous example in FIG. 12 is combined with 0.5 MW of PV(solar-photovoltaic) generation. The horizontal axis shows the time inthe 24-hour cycle. The left vertical axis shows megawatt hours. Theright vertical axis shows price in dollars per megawatt hours. The load910 is the electric load on the facilities. The import of power 920shows the power imported into the facilities from the grid. The battery930 shows the three bars below the horizontal axis for the powerdischarge from the batteries at specific times. The diesel 940 is notshown because diesel generation is not used in this co-optimizationbecause of its relative price. The solar 950 shows the power used by thesystem and/or stored in the batteries from the solar generator orphotovoltaic generator at various times. The LMP line 960 shows thefluctuating price for electricity during the 24-hour cycle.

Example Energy Storage Assets

Various examples are technology agnostic and can optimize any storageinstallation. However, certain forms of storage, such as compressed airand ice storage, are currently not recognized as applicable resourcesfor some regulation markets.

Aided by significant private investment, grid-scale batteries havesignificantly reduced in cost over the past decade. Differenttechnologies appear to have converged around a similar price: withbatteries offered at roughly $1-2 per Watt, and $1-2 per Watt-hour,before Balance of Plant (“BoP”) costs. (Watts [W, kW, MW] are a measureof power, i.e., the charge and discharge rate of an energy storageasset. Watt-hours [Wh, kWh, MWh] are a measure of energy, i.e., thestorage capacity of an energy storage asset.) At these prices, energystorage asset owners and lessees can use examples to achieve a positivereturn over the installed life while meeting their sites' backup needs.

Below is a brief overview of each different types of energy storageassets:

Lithium-Ion Battery

This “power battery” is well-suited for regulation with high efficiencyand hybrid opportunities. However, it has a high cost and little dataexists to corroborate lifespan claims.

Quoted prices include $2 million for a 1 MW/1 MWh unit, and $1.5 millionfor a 1 MW/250 kWh unit.

Lithium-Ion (Li-Ion) batteries are receiving great attention becausethey are the preferred battery for electric vehicles. Presently, Li-Ionbatteries are among the most expensive of the storage options available.This may change, as many companies are pouring resources into new Li-Ionvariants; however, some suggest that the chemical characteristics ofLi-Ion cells make it difficult to significantly reduce their cost.Additionally, Li-Ion is a new technology so that no company hasempirically demonstrated Li-Ion's lifespan. Companies have tried toallay these concerns through “accelerated testing” that charge/dischargethe battery more rapidly, but this does not provide full insight intohow well Li-Ion batteries perform over time.

Li-Ion batteries are very dense and therefore very small compared toother technologies. One manufacturer's 1 MW/1 MWh unit, for example, hasdimensions of 8′×20′. In comparison, a quoted lead-acid unit withsimilar specs has dimensions of 40′×70′.

Lithium-Ion's hybrid opportunities are discussed in the flow batterysection.

Lead-Acid Battery

This battery is the lowest-cost option with long lifespan and proventechnology. However, it is physically large with high maintenance andlimited depth of discharge.

Quoted prices include $896,000 for a 1 MW/2 MWh unit, and $512,000 for a1 MW/500 kWh unit.

Lead-Acid batteries, which have the same chemistry as a car battery, areproven for long-lasting grid applications. One manufacturer's 1 MW/1.4MWh unit lasted for 12 years, from 1996-2008, as both a provider ofvoltage support and a backup power source, before the battery cells werereplaced. The original power electronics of that installation stillfunction, and the unit is running with a new set of lead-acid cells.

A downside of lead-acid batteries is that they are very heavy and verylarge. This is why they are not being considered as much for EVs, andthis poses other logistical challenges for metropolitan installations.Lead-acid batteries are also considered to be high maintenance. Theyneed to be kept within a narrow temperature range, and therefore requiretheir own building (for industrial power uses), as well as periodicupkeep. Also, lead-acid batteries are typically oversized becauseexceeding the lower bounds of their state of charge can damage thecells. They are best for regulation or voltage support, and as backup ifsized explicitly for that purpose.

Flow Batteries

These batteries can be fully charged and discharged without damage tothe battery. Also, “hybridization” is possible. However, this “energybattery” limits regulation market opportunities and has low round-tripefficiency.

Quoted prices include $1.15 million for a 1 MW/1 MWh battery.

Flow batteries are energy batteries, i.e., they are best suited forbackup electricity, but their chemistry limits their ability to providehigh-MW regulation. The typically configured flow battery takes 4 hoursto charge/discharge, and flow batteries have lower round-tripefficiencies than other types (roughly 75% in contrast to Li-Ion's 90%).With flow batteries, a tank is filled with electrolyte fluid that flowsthrough solid cell stacks located at the top of the unit. The liquidsolution never degrades, but the cells need to be replaced every 5 or 6years. The cost of cell replacement is 10-15% of the total unit.

The electrochemical characteristics prohibit them from power-denseapplications, unless they are oversized and paired with a largeinverter, or “hybridized” with another battery technology. Hybridizationcan be provided by some suppliers in conjunction with a well-establishedpower electronics provider. One manufacturer has created a system thatallows its “energy” batteries to be paired with “power” batteries, likelithium-ion, connected through a single inverter. A leading lithium-ionbattery manufacturer recently announced a plan to provide a similarLi-Ion/flow battery unit for grid-scale applications.

Dry Cell Technology

This power battery is good for the regulation market. However, it hasvery small recommended depth of charge/discharge and is expensive.

Quoted prices include $1.5 million for a 1.5 MW/1 MWh battery, plus 30%extra for BoP (“Balance of Plant”).

These batteries provide high power-to-energy ratios that make themattractive for regulation, so long as they remain within a fairly narrowrange of state of charge. These batteries are not meant to fully chargeor discharge and pushing their recommended operating parameters affectstheir lifespan. Ideal state of charge is 20-80%. Because of theseconstraints, these batteries would need to be oversized to providebackup. These batteries are more expensive than cheaper options such aslead-acid.

Based on their characteristics, these batteries are likely suited forprojects whose primary objective is not backup power, but rather systemssupport. They provide high-MW regulation, can address voltage sagconcerns, and can be recharged by regenerative braking. However, whentheir state of charge limitations are taken into account, they appear tobe a costly technology, even in comparison to lithium-ion.

Ice Units

The thermal storage capacity of an ice unit can be used according to theprinciples herein as an energy storage asset.

Ice units can be used to modify how a building is cooled, including howenergy is consumed for cooling/air conditioning. An ice unit generallyconsists of a thermally-insulated storage tank that attaches to abuilding's air-conditioning system. The unit makes ice (generally atnight when supply costs tend to be lower) and uses that ice during theday to deliver cooling directly to the building's existing airconditioning system. Storage tanks can be on the order of hundreds ofgallons of water (e.g., about 450 gallons) of water. The water is frozenby circulating refrigerant through copper coils within or surroundingthe tank. The condensing unit then turns off, and the ice is storeduntil its cooling energy is needed. During the higher temperaturedaytime hours, the power consumption of air conditioning and demandlevels on the grid, increase. The ice unit may be used to replaces theenergy-demanding compressor of a building's air conditioning unit. Themelting ice of the ice unit, rather than the air conditioning unit, canbe piped around the building to cool it.

Compressed Air

The thermal storage capacity of compressed air can be used according tothe principles herein as an energy storage asset.

Using a heat exchanger, it is possible to extract waste heat from thelubricant coolers used in types of compressors, and use the waste heatto produce hot water. Depending on its design, a heat exchanger canproduce non-potable or potable water. When hot water is not required,the lubricant can be routed to the standard components for lubricantcooling. The hot water can be used in central heating or boiler systems,or any other application where hot water is required. Heat exchangersalso offer an opportunity to produce hot air and hot water, and allowthe operator some flexibility to vary the hot air to hot water ratio.

Controller for an Energy Storage Asset

The controllers for the energy storage assets described herein can beused to vary the input to or output from the energy storage assets. Whenthe controller functions as a converter, it converts the AC signal to aDC signal. That DC signal may be used to charge the energy storageasset. When the controller functions as an inverter, it converts onetype of voltage (direct current (DC)) into another type of voltage(alternating current (AC)). Since the electricity supplier generallysupplies 110 or 220 volts AC on the grid, the conversion may typicallybe from 12 volts DC to 110 or 220 volts AC. In another example, theoutput of the controller may be different, depending on the type of loadon the system. Inverters called utility intertie or grid tie may connectto energy generating assets such as solar panels or wind generator, andcan feed their output directly into the inverter. The inverter outputcan be tied to the grid power.

In a non-limiting example, the inverter takes the DC output from theenergy storage asset and runs it into a number of power switchingtransistors. These transistors are switched on and off to feed oppositesides of a transformer, causing the transformer to think it is gettingan AC signal. Depending on the quality and complexity of the inverter,it may put out a square wave, a “quasi-sine” (sometimes called modifiedsine) wave, or a true sine wave. The quality of the quasi-sine wave canvary among different inverters, and also may vary somewhat with theload.

The virtual partitioning of the energy storage asset describedfacilitates partitioning between energy and regulation participation.The partitioning can be based on the available capacity of thecontroller (i.e., the inverter/converter). The SOC of the energy storageasset may be used to provide a constraint within the optimization fordetermining the optimal charge/discharge strategy for participation inthese two different markets. As a non-limiting example, an operatingschedule generated according to the principles herein can indicate theoptimal charge/discharge strategy for the controller, including on anhourly basis, in response to or anticipation of projected LMPs. Thebalance of the inverter capacity of the controller may be made availableto the regulation market at its shorter timescales (e.g., at the2-second or minute-by-minute time intervals described above). Theproportion of the controller output (and hence the energy storage asset)committed to the energy market and the remaining proportion of theenergy storage asset committed to the regulation market are co-optimizedbased on the economic benefit derived from the two markets, and subjectto the SOC constraints. The operating schedules generated based on anyof the principles described herein, and in any of the example, cansuggest the proportion of the controller output committed to the energymarket and to the regulation market in a given time interval t (lessthan time period T), and for what length of time. the proportion of thecontroller output committed to the energy market and to the regulationmarket in a given time interval t (less than time period T). Forexample, for a controller with a 1 MWatt inverter capacity, theprinciples herein can be used to generate an operating schedule thatsuggests the proportion of the controller's 1 MWatt inverter capacitythat can be committed to the energy market and to the regulation marketin a given time interval t to generate the energy-related revenue.

Energy Generating Assets

Examples of energy generating asset applicable to the apparatuses andmethods herein include photovoltaic cells, fuel cells, gas turbines,diesel generators, flywheels, electric vehicles and wind turbines.

Electric storage has the potential to address some of the attributes ofrenewable energy generation. The intermittent nature of energygenerating assets, including solar generation, may present somedifficulty for grid operators. For example, weather events can makeenergy output of energy generating assets, including photovoltaic cellsor wind turbines, difficult to predict. As renewable generators make upa growing share of regional generation portfolios, grid operators mayrequire greater real-time visibility of distributed generation andbenefit from a resource's ability to control bi-directional power flow.Adding storage to distributed generation achieves new levels ofresponsiveness not seen with existing systems.

According to principles described herein, the operating schedulegenerated for a system that includes a controller, an energy storageasset and an energy generating asset can firm up intermittent renewablegeneration into dispatchable generation. The operating schedule canprovide for renewable generation forecasting based on the forecastedweather conditions.

Dynamic virtualization can be beneficial to sites that utilize bothenergy storage assets and energy generating assets. For example, byintegrating weather data, price forecasts, and expected site load,examples can accurately predict a solar array's output, determine howmuch solar generation should be captured by an energy storage asset, anddispatch the energy storage asset at the time of day that optimizesrevenues derived from wholesale market participation.

By passing energy through an energy storage asset and exhibitingreal-time control, power can be delivered strategically and act as aprice-responsive resource in the various wholesale markets. In effect,storage allows the maturation of energy generating assets as a resourcethat provides discrete power-flow to the grid that is controllable,quantifiable, and dispatchable. Solar power's best known challenge iscost. Through dynamic virtualization the value of renewable generationis increased by improving the resource with electric storage.

Example Implementation

FIG. 14 illustrates a flow diagram of a method according to one exampleof the present disclosure. Historical data 102 from a customer'sfacility is inputted into the system to calculate the RTO systemoperator's estimate of the customer baseline (CBL) 112 usage ofelectrical energy. This is the historically expected customer use ofelectricity, if the energy optimization is not applied, or calculated bythe RTO operator. This CBL calculation 112 is inputted to the system tocalculate a BAU (business as usual) electrical energy forecast 114 forthe facility, which forecasts the energy usage if the energy managementof the present system is not used. Alternatively, an alternate customerbaseline 130 may be calculated or modeled (e.g., by a user or operatorof a system according to the present disclosure), in place of the RTOsystem operator's calculation of the customer baseline 112, to be usedfor the BAU load forecast 114. Additional details of CBL modelingaccording to one example of the present disclosure are provided furtherbelow.

The system prepares data 116 so that the system may display an hourlydefault schedule and parameters 132 based on the CBL. This defaultschedule 132 is then transmitted to the end user's of electricity atfacilities 134. The end user 134 preferences, objectives and constraints136 for their energy use are then input. These user preferences,objectives and constraints 136 together with the data 116 from the CBLand BAU load forecasts 112, 114 and the resulting data 116 are used togenerate a renewable energy forecast 118. This renewable energy forecast118 can then be recycled to calculate an updated BAU load forecast 114.

The system also obtains a weather feed from the weather bureau 104 forinput into the calculation of the BAU load forecast 114.

The system also stores a default schedule and parameters 106 for thepreparation of data 116, as needed.

Various examples may also obtain price forecasts from a service bureau108 to inform the calculation of an optimal generation/load schedule(unconstrained) 120. These schedules 120 are used to develop feederschedules 138, which are delivered to the RTO grid and facilities microgrid operators 140. The operator 140 then provides a feeder constraintor violations analysis 142 which is used by the system to calculate anoptimal generation/load schedule (constrained) 122. This schedule 122 isthen used to calculate net costs (profits) 124 for application byexamples of the system. These net costs and profits 124 then are used todisplay the TREF (reference temperature, i.e. the target temperature forthe facility), load shedding schedule and prices 144. These displays arethen available to the end users of the electricity and of the system146. The end users 146 may then accept or modify the user's preferences148. These schedules may be accepted 126 and those accepted schedulesare transmitted 128 to the next step and used to calculate a day aheadvirtual generation schedule 210, as shown as FIG. 15. If the schedulesare not accepted 126, then the input parameters are adjusted 110, andrecalculation is performed on the optimal generation/load schedules(constrained) 122, and the process is reiterated until all schedules areaccepted at 126 and transmitted at 128 to calculate a day ahead virtualgeneration schedule 210.

FIG. 15 shows further examples of a method. Customer baseline CBL 202 isused to calculate the day ahead virtual generation schedule 210, whichalso uses the accepted schedules 126. This schedule data is then used todisplay hourly schedules, prices, and costs for the facility 212. Theschedules 212 are used to show hourly schedules, or other time periodbreakdowns, and prices and costs 224, which are transmitted to scheduler226. Scheduler 226 may accept or modify these schedules and prices 228.If the prices are accepted 214, then day ahead (DA) versus real-time(RT) bidding strategy 206 is developed. If the schedules 224 are notaccepted 214, then the system adjusts inputs and reoptimizes theschedule at 204, to recalculate the day ahead virtual generationschedule 210 and the process is reiterated until the schedules 224 areaccepted at 214. The bidding strategy 206 results in a final bid andsubmission to the day ahead market 216. This generates a bid that isbroken down by hourly, or other time period, schedules and prices 230,and sent to a market operator 232. The market operator 232 may accept ormodify (by 4 PM) the finalized bid 216, at 234. The system may thenrevise or modify (scheduler reviews and modifies) 218 the accepted ormodified bids. The system may adjust inputs and reoptimize the schedulesin 208, if necessary. A reliability run for revised bids may besubmitted 220 (those bids that have not been accepted in the day ahead).These revised bids may result in revised hourly schedules and prices236, and then they are resubmitted to the market operator 238. This mayresult in generation of final schedules 222, which results in ageneration of consumer reports 240 that are delivered to the end usersof electricity 242.

FIG. 16 shows a general overview of an example of one possible algorithmto suggest schedules for control of various energy assets at acustomer's facility using “optimal control” techniques and parametricestimation. In general, complex processes are often described bynonlinear equations, which present a challenge to the most advancedoptimization engines. The objective of various examples is to provide anaccurate CBL model represented by linearized equations, where thecoefficients of the linearized equations are adjusted in real-time fromactual process measurements, using parametric estimation. This methodmay provide an accurate load forecast, with minimal effort necessary todeploy the solution. In addition, the model may be adapted over time tophysical changes in the building, such as efficiency improvements.

A. Model of Customer Baseline Usage

One aspect of examples is the establishment of a “customer baseline”.The customer baseline is the level of a facility's consumption ofelectric energy on a given day, without regard to any action taken inresponse to price. That is, the customer baseline corresponds to thecustomer's energy consumption resulting from business-as-usual operationof its facility. Instead of relying on historical energy consumptiondata, the calculation of the customer baseline is based upon a computersimulation model of a facility's energy consumption, taking into accountits operating plans. Thus, the calculation is predictive rather thanbackward-looking.

A mathematical simulation model is developed for each facility, takinginto account the facility's energy consuming equipment and its operatingplans. In FIG. 16, module 314 contains the linearized simulation model(Instance ‘A’) of the CBL load, as generated, for example, using modelbuilder module 502 in FIG. 18, discussed further below. The calculationof consumption for each day may reflect all of the known relevantvariables, such as building materials, thermal properties of thebuilding or buildings, building occupancy, desired temperature, ambienttemperature, and operations for the day. At least the followingparameters may be included: HVAC building settings and controls,identification of interruptible loads and their pre-defined response toa price signal, and desired temperatures. The software retains a recordof the actual demand response action taken by an end-user.

The model for a facility can be composed of a group of sub-models of allthe facility's energy-consuming elements, shown in components library503, in FIG. 18 herein. The examples below refer to a building load, butthe same method can be applied to any device, such as a motor orlighting fixture. Variable load as well as interruptible load equipmentmay be modeled specifically. Items constituting a fixed load may bemeasured and modeled individually.

Building thermodynamics is pertinent in the determination of electricalloads. The fundamental thermodynamic equations for this application are:

$\begin{matrix}{{{CpM}\frac{\mathbb{d}T}{\mathbb{d}t}} = {{Q\_ in} + {Q\_ body} - {Q\_ hvac} - {Q\_ chill} - {Q\_ vent}}} & (1)\end{matrix}$

Where:

CpM=Energy-temperature change ratio.

Q_in=Energy inflow due to the difference between building internaltemperature and ambient temperature.

Q_body=Energy emission from people and equipment in the building.

Q_hvac=Energy inflow from the HVAC in addition to the chiller andventilation.

Q_chill=Energy inflow from the chiller.

Q_vent=Energy inflow from the ventilation system.Q_in=UA_build×(T ^(A) −T ¹)  (2)

Where:

Q_in=Energy inflow due to the difference between building internaltemperature and ambient temperature.

UA_build=Heat energy transfer rate due to temperature differences.

T^(A)=Ambient temperature outside the building.

T¹=Internal temperature of the building.Q_body=Num_people×(Q_per_body+(equip_rate×Q_equip))  (3)

Where:

Q_per_body=Amount of energy emitted per hour from a person present inthe building.

Num_people=Number of people present in the building.

equip_rate=Rate of personal electronic equipment per person.

Q_equip=Average amount of energy emitted by electronic equipment such ascell phones and computers.

$\begin{matrix}{{Q\_ hvac} = {\frac{u\_ hvac}{k\_ const} \times {MaxQ\_ hvac} \times \left( {T^{1} - {T\_ cool}} \right)}} & (4)\end{matrix}$

Where:

Q_hvac=Energy inflow from the HVAC in addition to the chiller andventilation.

u_hvac=HVAC loading.

MaxQ_hvac=Maximum thermal production capacity of the HVAC.

T_cool:=Defines the threshold temperature below which the HVAC systemoperates in heating mode, while above which it operates in cooling mode.

T¹=Internal temperature of the building.

k_const=Constant parameter.Q_vent=MaxQ_vent×U_vent  (5)

Where:

Q_vent=Energy inflow from the ventilation system.

u_vent=HVAC ventilation loading.

MaxQ_vent=Maximum thermal production capacity of the HVAC ventilation.

$\begin{matrix}{{Q\_ chill} = {{\frac{u\_ chill}{k\_ const} \times {MaxQ\_ chill} \times \left( {T^{1} - {T\_ cool}} \right)} + {{u\_ dice} \times {Ice\_ drate} \times {Btu\_ MWh}{\_ ConvRate}}}} & (6)\end{matrix}$

Where:

Q_chill=Energy inflow from the chiller.

u_chill=HVAC chiller loading.

u_dice=Cooling use of stored ice.

MaxQ_chill=Maximum thermal production capacity of the HVAC chiller.

Ice_drate=Chiller's ice-consuming rate when the stored ice is to be used(discharge).

T¹=Internal temperature of the building.

k_const=Constant parameter.

Btu_MWh_ConvRate=Conversion coefficient of electric to heat energy.

T_cool=Defines the threshold temperature below which the HVAC systemoperates in heating mode, while above which it operates in cooling mode.

The thermodynamic equations are related to electrical load through thefollowing equations.

$\begin{matrix}{{MW\_ hvac} = {\frac{MaxQ\_ hvac}{{Eff\_ hvac} \times {Btu\_ mWh}{\_ ConvRate}} \times {u\_ hvac}}} & (7)\end{matrix}$

Where:

MW_hvac=Average HVAC power consumption.

Eff_hvac=Efficiency coefficient of HVAC thermal energy production byelectric energy.

Btu_Mwh_ConvRate=Conversion coefficient of electric to heat energy.

MaxQ_hvac=Maximum thermal production capacity of the HVAC.

u_hvac=HVAC loading.

$\begin{matrix}{{MW\_ vent} = {\frac{MaxQ\_ vent}{{Eff\_ vent} \times {Btu\_ mWh}{\_ ConvRate}} \times \;{u\_ vent}}} & (8)\end{matrix}$

Where:

MW_vent:=Average ventilation power consumption.

MaxQ_vent=Maximum thermal production capacity of the HVAC ventilation.

Eff_vent=Efficiency coefficient of HVAC thermal energy production byelectric energy.

Btu_MWh_ConvRate=Conversion coefficient of electric to heat energy.

$\begin{matrix}{{MW\_ chill} = {{\frac{MaxQ\_ chill}{{Eff\_ chill} \times {Btu\_ mWh}{\_ ConvRate}} \times {u\_ chill}} + {{u\_ cice} \times {Ice\_ crate}}}} & (9)\end{matrix}$

Where:

MW_chill=Average chiller power consumption.

MaxQ_chill=Maximum thermal production capacity of the HVAC chiller.

Eff_chill=Efficiency coefficient of the HVAC chiller.

u_cice=Ice-making operation.

Ice_crate=Chiller's ice-making rate when making ice (charge).

u_chill=HVAC chiller loading.

Btu_MWh_ConvRate=Conversion coefficient of electric to heat energy.Load_hvac=MW_hvac+MW_vent+MW_chill  (10)

Where:

Load_hvac=Total electric power to operate the HVAC system.

MW_hvac=Average HVAC power consumption.

MW_vent=Average ventilation power consumption.

MW_chill=Average chiller power consumption.

The variables Num_people and equip_rate in equation (3) are determinedfrom occupancy data and facility or industry data concerning the numberand types of electronic equipment per person. MaxQ_hvac, MaxQ_chill, andMaxQ_vent, can be determined from equipment name plate data.

The model established for an energy-consuming facility, and thesub-models for related equipment may take into account the abovethermodynamic load equations.

There is a wide variety of other types of variable load andinterruptible load equipment that can be accurately modeled using asimilar approach. The granularity of these models will be that necessaryfor accurate calculation of the business as usual load of a facility asmeasured against the metered load. Sub-metering can be used as necessaryto validate mathematical models of variable and interruptible loads.

For large scale facilities consisting of multiple buildings or elements,the total customer base line load is simply the sum of the base lineloads for the individually-modeled aggregated elements.

The process for developing the model of a facility is iterative. Ageneric, or representative, model of the facility is first developed.Experiments are then performed on the building or buildings to determinetheir thermal parameters. Sub-metering is used as previously mentioned.The experimental results and load data are incorporated to modify andtune the generic model.

After the model is created, it is validated by conducing simulations ofthe facility using the model to calculate the electrical load. Modeloutput is compared to actual historical metered loads. Furtherexperimentation, data collection, and model refinement is performeduntil the model accurately reproduces metered data.

B. Optimization

As noted above, one of the goals of the implementation shown in FIG. 16is the generation of one or more control signals (i.e., a “controlvector”) representing a suggested schedule for control of various energyassets at a customer's facility so as to improve energy usage relativeto a customer base line, based on a variety of factors. According to oneexample, “optimal control” techniques are employed to optimize energyuse based at least in part on cost of energy considerations.

1. Overview of Optimization

An optimal value of a control vector u is that which minimizes totalcost and provides maximal benefit to the user. Various examples utilizesystem observation, faster-than-real-time numerical simulation,mixed-integer optimization, and remote hardware actuation to performautomated load demand response and create “virtual generation”.

Various examples utilize advanced mathematical techniques to performreal-time optimization of load behavior for energy cost minimization.Various examples perform a process that is divided in to five steps, asoutlined in FIG. 17:

1) discretization—conversion of the continuous system model to adiscrete-time representation;

2) initialization of u k—like many nonlinear analyses, initializationfacilitates convergence;

3) system observation—acquisition of x ^((m))(t₀) via physicalmeasurement and v ^((m)) external communication network;

4) cost minimization—determination of the value of u (referred to as u_(min)) which results in minimal total cost, as defined by the objectivefunction (c_(Δ)); and

5) system actuation—generation of control signals based on results ofcost minimization, specifically u _(min).

2. Mathematical Definition of System for Optimization

Various examples utilize an ordinary differential description of theaggregate load system—derived from the laws of energy conservation andapplicable laws of physics—like that shown below, employing thefollowing variables: set of ordinary differential equations describingdynamic behavior (f), set of algebraic expressions describing staticbehavior (g), system state vector (x), and system parameter vector (u),and time (t).

$\begin{matrix}{\underset{\_}{\overset{.}{x}} = \overset{\overset{{\mathbb{d}\underset{\_}{x}}/{\mathbb{d}t}}{︷}}{f\left( {\underset{\_}{x},\underset{\_}{u},t} \right)}} & (11) \\{\underset{\_}{y} = {g\left( {\underset{\_}{x},\underset{\_}{u}} \right)}} & (12)\end{matrix}$

A set of objective sub-functions (c_(i)) is utilized to quantify theoptimality of u with respect in terms of several systemcharacteristics—e.g. electric cost, natural gas fuel cost (for DG's),differential between actual and desired internal temperature,differential between actual and desired lighting status (on/off). Notethe following definition: set of external inputs (v) supplied by thelocal network operator.objective sub-function=c _(i)( x,y,u,v,t)  (13)

These objective sub-functions are user-defined, derived from the loadbehavior. Refer to the examples below.c _(i)=desired temperature−actual temperaturec _(i)=(fuel cost per W)(W generated by DG)c _(i)=(electricity cost per W)(W consumed)  (14)

The main objective function (c) examines cost over a defined timeinterval—t₀ to t_(T)—and takes the form of a integral weighted sum, witheach term representing an individual penalty. Weighting coefficients(α_(i)) are also user-defined on the basis of desired balance betweencomfort, productivity, and energy cost. Refer to the expression below.

$\begin{matrix}{{c\left( {\underset{\_}{x},\underset{\_}{y},\underset{\_}{u},\underset{\_}{v},t_{K}} \right)} = {\int_{t_{0}}^{t_{K}}{\left\lbrack {\sum\limits_{i = 1}^{n}\;{\alpha_{i}*{c_{i}\left( {\underset{\_}{x},\underset{\_}{y},\underset{\_}{u},\underset{\_}{v},t} \right)}}} \right\rbrack\ {\mathbb{d}t}}}} & (15)\end{matrix}$

Whenever possible, the system model—presented in (11) and (12)—should belinearized such that a closed-form solution exists. This may beaccomplished in two ways:

1) piece-wise linearization—a more basic approach, in which thenonlinear model is estimated via first-order approximation for a set ofdiscrete operating points; and

2) adaptive model—the coefficients of a linear model are assumed to befunctions of time, estimated periodically from real-time systemobservation and application of Kalman Filters.

3. Discrete Simulation

Methods in accordance with various examples require discretization ofthe continuous system dynamic model/objective function via trapezoidalrule, or similar scheme. This facilitates the conversion of continuousdifferential expressions (f) to discrete difference expressions (f_(Δ)).Refer to (16) through (19).

$\begin{matrix}{t_{\lbrack k\rbrack} = {k\left( {\Delta\; t} \right)}} & (16) \\\begin{matrix}\overset{{note}\mspace{14mu}{that}\mspace{14mu}{f{(t)}}\mspace{14mu}{abbreviated}}{{representation}\mspace{14mu}{of}\mspace{14mu}{f\left( {\underset{\_}{x},\underset{\_}{u},t} \right)}} \\\overset{︷}{{f(t)} = {f\left( {\underset{\_}{x},\underset{\_}{u},t} \right)}}\end{matrix} & (17) \\\begin{matrix}{{\underset{\_}{x}(t)} = {{\int_{t_{0}}^{t}\left\lbrack {{f\left( {\underset{\_}{x},\underset{\_}{u},t} \right)}\ {\mathbb{d}t}} \right\rbrack} + {\underset{\_}{x}\left( t_{\lbrack 0\rbrack} \right)}}} \\{\approx {\ldots\mspace{14mu}\ldots}} \\{\approx {{\frac{1}{2}{\sum\limits_{k = 1}^{({{t/\Delta}\; t})}\;{\underset{\underset{{f{({\underset{\_}{x},\underset{\_}{u},t_{\lbrack k\rbrack}})}} + {f{({\underset{\_}{x},\underset{\_}{u},t_{\lbrack{k - 1}\rbrack}})}}}{︸}}{\left\lbrack {{f\left( t_{\lbrack k\rbrack} \right)} + {f\left( t_{\lbrack{k - 1}\rbrack} \right)}} \right\rbrack}\Delta\; t}}} + {\underset{\_}{x}\left( t_{\lbrack 0\rbrack} \right)}}}\end{matrix} & (18) \\\begin{matrix}{0 = {f_{\Delta}\left( {\underset{\_}{x},\underset{\_}{u},{\Delta\; t},t} \right)}} \\{= {\ldots\mspace{14mu}\ldots}} \\{= \begin{pmatrix}{{x\left( t_{\lbrack 1\rbrack} \right)} - \left\lbrack {{{\frac{1}{2}\left\lbrack {{f\left( t_{\lbrack 1\rbrack} \right)} + {f\left( t_{\lbrack 0\rbrack} \right)}} \right\rbrack}\Delta\; t} + {\underset{\_}{x}\left( t_{\lbrack 0\rbrack} \right)}} \right\rbrack} \\{{x\left( t_{\lbrack 2\rbrack} \right)} - \left\lbrack {{{\frac{1}{2}\left\lbrack {{f\left( t_{\lbrack 2\rbrack} \right)} + {f\left( t_{\lbrack 1\rbrack} \right)}} \right\rbrack}\Delta\; t} + {\underset{\_}{x}\left( t_{\lbrack 1\rbrack} \right)}} \right\rbrack} \\{\left( t_{\lbrack 3\rbrack} \right) - \left\lbrack {{{\frac{1}{2}\left\lbrack {{f\left( t_{\lbrack 3\rbrack} \right)} + {f\left( t_{\lbrack 2\rbrack} \right)}} \right\rbrack}\Delta\; t} + {\underset{\_}{x}\left( t_{\lbrack 2\rbrack} \right)}} \right\rbrack} \\\vdots\end{pmatrix}}\end{matrix} & (19)\end{matrix}$

It also facilitates discretization of the objective function (c). Referto (20) and (21).

$\begin{matrix}\begin{matrix}\overset{{note}\mspace{14mu}{that}\mspace{14mu}{c_{i}{(t)}}\mspace{14mu}{abbreviated}}{{representation}\mspace{14mu}{of}\mspace{14mu}{c_{i}\left( {\underset{\_}{x},\underset{\_}{y},\underset{\_}{u},\underset{\_}{v},t} \right)}} \\\overset{︷}{{c_{i}(t)} = {c_{i}\left( {\underset{\_}{x},\underset{\_}{y},\underset{\_}{u},\underset{\_}{v},t} \right)}}\end{matrix} & (20) \\\begin{matrix}{{c\left( {\underset{\_}{x},\underset{\_}{y},\underset{\_}{u},\underset{\_}{v},t} \right)} = {\int_{t_{0}}^{t}{\left\lbrack {\sum\limits_{i = 1}^{n}\;{\alpha_{i}*{c_{i}(t)}}} \right\rbrack\ {\mathbb{d}t}}}} \\{\approx {\ldots\mspace{14mu}\ldots}} \\{\approx \underset{\underset{c_{\Delta}({\underset{\_}{x},\underset{\_}{y},\underset{\_}{u},\underset{\_}{v},t,{\Delta\; t}})}{︸}}{\frac{1}{2}{\sum\limits_{k = 1}^{({{t/\Delta}\; t})}{\left\lbrack {\sum\limits_{i = 1}^{n}\;{\alpha_{i}*\left\lbrack {{c_{i}\left( t_{\lbrack k\rbrack} \right)} + {c_{i}\left( t_{\lbrack{k - 1}\rbrack} \right)}} \right\rbrack}} \right\rbrack\Delta\; t}}}}\end{matrix} & (21)\end{matrix}$

However, it should be noted that these approximations might only holdtrue for small discrete time steps (Δt≈0).

4. Initialization

The first step of a process in accordance with various examples, isinitialization of the vector to be optimized (u). This initial conditionis represented as u ⁽⁰⁾, or the 0^(th) iteration of u. Note that properinitialization is a requirement of most nonlinear system analysismethods.

A second step—generally performed in parallel with the first—isobservation of the current system state (x(t_(o))) as well as collectionof any other relevant data (v).

5. Optimization/Cost Minimization

In an implicit approach, the discrete system model (f_(Δ)) and objectivefunction (c_(Δ)) are solved as a single entity, allowing the user tominimize cost and simulate the load response simultaneously. Theweighting coefficients β₁ and β₂ may be utilized to place emphasis onsimulation accuracy over cost minimization. Refer to (22).

$\begin{matrix}{\min\begin{Bmatrix}{\beta_{1}*\overset{\overset{{for}\mspace{14mu}{dynamic}\mspace{14mu}{simulation}}{︷}}{f_{\Delta}\left( {\underset{\_}{x},\underset{\_}{u},{\Delta\; t},t_{k}} \right)}} \\{\beta_{2}*\underset{\underset{{for}\mspace{14mu}{cost}\mspace{14mu}{minimization}}{︸}}{c_{\Delta}\left( {\underset{\_}{x},\underset{\_}{y},\underset{\_}{u},\underset{\_}{v},t,{\Delta\; t}} \right)}}\end{Bmatrix}} & (22)\end{matrix}$

Various examples, however, utilize an explicit approach in whichsimulation and cost minimization occur consecutively—significantlyreducing the number of expressions to be optimized. Refer to (23).

$\begin{matrix}\overset{\overset{{{note}\mspace{14mu}{that}\mspace{14mu}{\underset{\_}{u}}_{\min}\mspace{14mu}{is}\mspace{14mu}{the}\mspace{14mu}{optimal}\mspace{14mu}{value}\mspace{14mu}{of}\mspace{14mu}\underset{\_}{u}},\mspace{14mu}{{that}\mspace{14mu}{which}\mspace{14mu}{minimizes}\mspace{14mu}{the}\mspace{14mu}{{obj}.\mspace{14mu}{function}}}}{︷}}{{c_{\Delta}\left( {\underset{\_}{x},\underset{\_}{y},{\underset{\_}{u}}_{\min},\underset{\_}{v},t,{\Delta\; t}} \right)} = {\min\left\{ {c_{\Delta}\left( {\underset{\_}{x},\underset{\_}{y},\underset{\_}{u},\underset{\_}{v},t,{\Delta\; t}} \right)} \right\}}} & (23)\end{matrix}$

Note that the optimal value of u, that which yields a minimal value ofc/c_(Δ) is denoted by the variable u _(min).

Generally, the objective function (c/c_(Δ)) is nonlinear and, as such, aclosed-form solution for u _(min) does not exist. To find u _(min), anonlinear optimization method can be employed. One example is thegradient search, an iterative method utilizing first-order approximationof system behavior to iteratively calculate a local minimum. Refer tothe update expression presented in (24).

$\begin{matrix}{{\underset{\_}{u}}^{({m + 1})} \approx {{- {{c_{\Delta}\left( {\underset{\_}{u}}^{(m)} \right)}\left\lbrack \frac{\mathbb{d}{c_{\Delta}\left( {\underset{\_}{u}}^{(m)} \right)}}{\mathbb{d}\underset{\_}{u}} \right\rbrack}^{- 1}} + {\underset{\_}{u}}^{(m)}}} & (24)\end{matrix}$

Note that the gradient method is based on a Taylor Series Expansion ofthe objective function, as shown in (25).

$\begin{matrix}{{c_{\Delta}\left( {\underset{\_}{u}}_{\min} \right)} \approx {\overset{\overset{\overset{operating}{point}}{︷}}{c_{\Delta}\left( {\underset{\_}{u}}^{(i)} \right)} + \overset{\overset{1^{st}\mspace{14mu}{order}\mspace{14mu}{term}}{︷}}{\frac{\mathbb{d}{c_{\Delta}\left( {\underset{\_}{u}}^{(i)} \right)}}{\mathbb{d}\underset{\_}{u}}\left( {{\underset{\_}{u}}_{\min} - {\underset{\_}{u}}^{(i)}} \right)}} \approx 0} & (25)\end{matrix}$

The explicit approach to cost minimization is performed, essentially, infour steps:

1) faster than real-time simulation—for each iteration (m), it isnecessary in various examples to examine, via simulation, how the loadsystem will respond to a set of parameters u ^((m));

2) cost evaluation/decision—for each iteration (m), it is necessary invarious examples to calculate total cost (c_(Δ));

3) fast optimization—for each iteration, it is necessary in variousexamples to update the set of system input (u ^((m+1))) for minimal cost(c_(Δ)); and

4) decision—if the incremental change between u ^((m+1)) and u ^((m)) issmall, then assume that a local minimum is found—otherwise, repeat loopwith simulation.

In many instances, the load composition may warrant use of amixed-integer u, in which at least one control parameter takes oninteger values only. One example is the actuation of lighting-typeloads, for which only two statuses exist—off (0) and on (1).

6. Kalman Filtering

The presence of noise in system observations is defined in (26).

$\begin{matrix}\overset{\overset{\overset{{observation}\mspace{14mu}{equals}}{{state}\mspace{14mu}{plus}\mspace{14mu}{noise}}}{︷}}{\underset{\_}{z} = {\underset{\_}{x} + \underset{\_}{ɛ}}} & (26)\end{matrix}$

To account for this noise, various examples utilize a Kalman filter intheir method. It is an efficient recursive filter utilized to estimatethe state of a linear dynamic system from a series of noisymeasurements. In contrast to batch estimation techniques, it is atime-invariant process.

The state of the filter is represented by two variables:

{circumflex over (x)} _(k|k): the a posteriori state estimate attime-step k given the observations up to and including time-step k; and

P_(k|k): the a posteriori error covariance matrix—measure of theestimated accuracy of {circumflex over (x)} _(k|k).

The Kalman filter operates in two phases:

1) Predict—the state estimate from the previous time-step is updated toestimate the current time-step. This predicted state estimate is knownas the a priori state estimate because, although it is an estimate ofthe state at the current time-step, it does not include observationinformation from the current time-step. Refer to (27). The followingvariables are referenced below: predicted state ({circumflex over (x)}_(k|k−1)), predicted estimate covariance (P _(k|k−1)),{circumflex over (x)} _(k|k−1) =F _(k)( {circumflex over (x)}_(k-1|k−1))+ B _(k-1)( u _(k-1))P _(k|k−1) =F _(k)( P _(k-1|k−1)) F _(k) ^(T) +Q _(k-1)  (27)

2) Update—the current a priori prediction is combined with currentobservation information to refine the state estimate—referred to as thea posteriori state estimate. Refer to (28). The following variables arereferenced below: innovation or measurement residual ({tilde over (y)}_(k)), innovation (or residual) covariance (S _(k)), optimal Kalman gain(K _(k)), updated state estimate ({circumflex over (x)} _(k|k)), updatedestimate covariance (P _(k|k)).{tilde over (y)} _(k) =z _(k) −H _(k) {circumflex over (x)} _(k|k−1)S _(k) =H _(k) P _(k|k−1) H _(k) ^(T) +R _(k)K _(k) =P _(k|k−1) H _(k) ^(T) S _(k) ⁻¹{circumflex over (x)} _(k|k) ={circumflex over (x)} _(k|k−1) +K _(k){tilde over (y)} _(k)P _(k|k)=(I−K _(k) H _(k)) P _(k|k−1)  (28)

Now, if the model is accurate, then the following invariant arepreserved and all estimates have a mean error of zero.E[x _(k) −{circumflex over (x)} _(k|k) ]=E[x _(k) −{circumflex over (x)}_(k|k−1)]=0E[{tilde over (y)} _(k)]=0  (29)

7. Virtual Generation

An aspect of various examples is that they give a user the ability todefine the desired load behavior as an objective function (c) andimplement it in a remote and automated fashion, without the need formanual observation, decision making, or actuation.

A simple objective function, composed of only two weighted penalties, ispresented in (30). The first is associated with comfort, quantified by adifference between the desired (T_(des)) and actual (T_(act)) internaltemperature. The second is associated with energy cost, quantified bythe product of electric cost (c_(W)) and consumption (W_(con)). The userexpresses his or her desired balance between comfort and energy cost asa set of weighting coefficients (α₁, α₂).

$\begin{matrix}\begin{matrix}{{c\left( {\underset{\_}{x},\underset{\_}{y},\underset{\_}{u},\underset{\_}{v},t_{K}} \right)} = {\ldots\mspace{14mu}\ldots}} \\{= {\int_{t_{0}}^{t_{K}}{\left\lbrack {{\alpha_{1}\overset{\overset{\overset{\overset{{penalty}\mspace{14mu}{associated}\mspace{14mu}{with}}{{difference}\mspace{14mu}{between}\mspace{14mu}{desired}}}{{and}\mspace{14mu}{actual}\mspace{14mu}{{temp}.}}}{︷}}{{{T_{act}(t)} - {t_{des}(t)}}}} + {\alpha_{2}\overset{\overset{\overset{{penalty}\mspace{14mu}{associated}}{{with}\mspace{14mu}{energy}\mspace{14mu}{cost}}}{︷}}{\left\lbrack {c_{W}(t)*{W_{con}(t)}} \right\rbrack}}} \right\rbrack\ {\mathbb{d}t}}}}\end{matrix} & (30)\end{matrix}$

Three sample cases are examined:

1) strict regulation of T_(act)—in the case of α₁>α₂, the optimizationalgorithm places emphasis on comfort over energy conservation, resultingin T_(act)≈T_(des).

2) strict regulation of W_(con)—in the case of α₁<α₂, the optimizationalgorithm places emphasis on energy conservation over comfort, resultingin W_(con)≈0.

3) even balance—in the case of α₁≈α₂, the optimization algorithm placesequal emphasis on comfort and energy conservation, resulting insemi-regulation of both T_(act) and W_(con).

The example demonstrates that, under certain circumstances and withproper configuration, examples may be utilized to regulate load powerconsumption and, in turn, emulate virtual generation. Note that avirtual generator is a set of components—e.g. load, energy storage,renewables—configured to mimic traditional supplies and participate, assuch, in economic dispatch.

C. System Implementation

Given the mathematical construct outlined above and illustrated in FIG.17, and with reference again to FIG. 16, the optimization engine (Module316) will iterate on the control vector u(t) which represents controlvariables (e.g., temperature control), and Module 314 will compute thecorresponding state vector x(t), which represents process variables(e.g., temperature, humidity) over time, taking into account variousinputs such as weather forecast parameters (Module 308) and PriceForecast Feed 306. The optimization engine (Module 316) iterates on thecontrol vector u(t) until the objective function (Module 320) isoptimized over the defined time period (e.g., next 24 hours). Theobjective function combines several user adjustable components thatinclude such factors as comfort, economic benefit, and environmentalobjectives, along with various time dependent constraints on both stateand control variables. Economic benefits are derived from known timedependent economic parameters, including the wholesale price forecast(Module 306). The solution is stored in the Optimization Database(Module 304), which contains various optimization scenarios or casesthat can be simulated and compared by the end user. Once a case isselected, the user will then commit the specific scenario to theReal-Time Database (Module 302).

The selected control vector u(t) may then be used by the BuildingManagement System to control the corresponding physical resources as afunction of time. The same control vector is submitted in parallel tothe Module 312, which contains an identical version of the BuildingModel (Instance ‘B’). The output of Module 312, the simulated state ofthe building x(t), is compared against the measured state xm(t), whichis produced by the Building Management System 310. The difference is fedto the Parametric Estimator (Module 318) which calculates, by doingparametric estimation (e.g., using Kalman filters), the modelcoefficients A(t) and B(t) that minimize the difference between thesimulated state and the observed state of the building. Thesecoefficients are updated periodically to ensure that the linearizedmodel used for the optimization (Module 314) forecasts accurately thetime dependent simulated behavior of the building in the vicinity of thecurrent measured state.

FIG. 18 describes examples of system modules for various examples of asystem. Each module may be a software module executed on hardware. Themodules are in electronic communication with each other as shown in FIG.18 to operate in the system.

Model builder module 502 models a particular client facility such as abuilding or office campus. The energy resources modeled may include thebuilding, the lights, HVAC, motors, electricity generation capacity,generators, and solar generators, for example. The model builder module502 and other technical elements 502 through 542 shown in FIG. 18 mayvariously run as software on PCs or other appropriate computerfacilities.

The components library 503 may be a library of software components tomodel particular genres of facilities or energy resources, such asbuildings, HVAC, motors, energy storage devices, batteries, solargenerators, and solar panels, which components 503 may be calibratedwith specific parameters for specific clients.

The generation forecast module 504 receives weather forecast informationfrom the weather forecast module 510, and receives electricity priceforecasts and related price forecasts, from the price forecast module512. The generation forecast module 504 then generates for the customera forecast of the customer's electricity generation, for example fromsolar generators, solar panels, or diesel generation.

The load forecast module 505 generates a forecast of load for a specificfacility, that is a forecast of the electricity demand used by thecustomer's facility, broken down for time periods over the day, forexample, in half hour increments.

The optimization module 506 produces optimum options for the individualcustomer, presenting tradeoffs for optimizing different parameters, suchas the total cost of electricity versus comfort from the maintainedtemperature. For example, there is a tradeoff in the summer monthsbetween the cool temperature generated within a facility by HVAC and theenergy costs to generate the same. In a dynamic virtualization exampledescribed herein, the optimization module 506 may produce a plan forcontrolling the operation of at least one of the facility's energyassets to reduce the electricity provider's overall charge to thefacility for electric energy, or to provide a revenue source to thefacility, the plan being produced on the basis of the model, andvariations in the price of electric energy during a day. The controlledassets are optimized in the plan across a number of energy markets,selected from the group comprising electric power, capacity, ancillaryservices, and regulation. Any energy storage assets are optimized in theplan by dynamic virtualization across the markets for power, capacity,ancillary services and regulation.

The power analytics module 507 analyses a micro electric grid (e.g. fora campus or a large building for a customer), and maintains acceptablepower quality within the forecasts and optimizations, for examplemaintaining required voltage and amps within acceptable tolerances.

The carbon calculator module 508 calculates how much the system optionspresented by optimization module 506 may each reduce the carbonfootprint of the client system.

The engineer 509 communicates with the various modules of the system 502through 508 to develop the forecasts and other output on a daily basis,perhaps disaggregated by hourly or lesser time periods.

The modules 502, 503, 504, 505, 506, 507 and 508 communicate with eachother in the system and with the engineer 509 in the optimization modeof the system to develop and analyze optimization options for the targetclient facility.

The weather forecast module 510 provides data which is purchased fromoutside vendors and the data is imported to the generation forecastmodule 504.

The price forecast module 512 also provides data bought from outsidevendors to import price forecast data to the generation forecast module504.

The monitor and control module 520 monitors the client's facilities todetermine if the customer actually operates facilities in the manner ofthe chosen option and also communicates with the grid operator 524. Themonitor and control module 520 also can be used to remotely control theclient's facility 540, if authorized, and if in electronic communicationwith the client's facility 540.

The process interface module 522 is similar to a communication API inelectronic communication between the monitor and control module 520 andthe gateway 526.

Gateway 526 is a gateway in electronic communication with the EMS/BMSSCADA module 540. The energy management system (“EMS”), and the buildingmanagement system (“BMS”), and the supervisory control and dataacquisition (“SCADA”) system are legacy systems installed in thecustomer's facilities that communicate through the gateway 526 to theirprocess interface module 522 and to the modules 502 through 508 of thesystem. The EMS/BMS SCADA module 540 communicates through the gateway526 to the process interface 522 through a variety of possiblecommunication links including, e.g., the Internet, which links mayinclude a virtual private network (“VPN”).

The facility manager 542 communicates with and controls the EMS/BMSSCADA module 540 through communication through his computer system.

The market/utility interface module 524 communicates with the carboncalculator 508 and the other system modules and the monitoring andcontrol module 520. Furthermore the market/utility interface 524communicates with the market operating/utility 534 and the dispatcher530. The dispatcher 530 communicates with the customer interface module532. The customer interface module 532 permits the dispatcher 530 tocommunicate with the customer facility manager 542.

The facilities manager 542 offers to produce power at a price, or tocontrol load to an extent. If this is accepted by the marketoperator/utility 534 at a particular price, then the facility 540consequently performs accordingly.

The market/utility interface 524 is similar to an API that communicatesbetween the system modules 502 through 508, and the marketoperator/utility 534, and the settlement module 528. The market/utilityinterface 524 communicates to the grid operator 534 that the dispatcher530 makes an offer to the operator 534 on behalf of the facility manager542 to produce electricity at a price and a time and a quantity, or toreduce consumption from the CBL (consumer base line) in a certain amountat a certain time. The operator 534 may then accept that offer. Thisinformation is then transmitted to the settlement module 528 to monitorspecific performance by the facility 540 to produce electricity orreduce consumption from the CBL as agreed, and to arrange billing andpayment accordingly between the market operator 534 and the facilitymanager 542.

The monitor and control module 520, the process interface module 522,the gateway 526, the market/utility interface 524, the settlement module528, and the customer interface 532 are part of the real-time modeoperation of the system. In the real-time mode, these modules monitorand control what the facility is actually doing, and also inform thefacility manager 542 and the dispatcher 530 of sudden changes in pricesthat may lead to an alteration of the optimization schedule.

The weather forecast module 510 and the price forecast module 512 areowned and operated by third parties. The EMS/BMS/SCADA module 540 isowned and operated by the customer. The optimization mode modules502-508 and the modules 520 and 522 are owned and operated by a companythat may be different from the customer and different from the marketoperator.

The engineer 509, weather forecast module 510, price forecast module512, market/utility interface 524, settlement module 528, dispatcher530, customer interface 532, facility manager 542, EMS/BMS/SCADA 540,and gateway 526, may communicate with the system 502, 503, 504, 505,506, 507, 508, 520, 522 and with each other through the Internet,wirelessly, by leased lines, POTS, VPN, or other telecom links.

FIG. 19 shows an example of optimization mode output for variousexamples. Electricity energy consumption and production features of acustomer's facilities are shown, such as HVAC 602, solar panels (2megawatts) 604, battery (5 megawatts hours) 606, gas fueled generator (5megawatts) 608, and diesel generator (5 megawatts) 610. These resources602 through 610 integrate over the power grid 612 with the larger RTOpower grid which is a source of imported power 614. Here the term“imported power” means electric power from the RTO brought into thecustomer's facility over the power grid 612.

Various optimization options, produced by the optimization module 506 inFIG. 18, are shown in FIG. 19 in columns 621, 622, 623, 624, 625 and626, and rows 630 through 646. Column 621 shows various row titlesincluding the date row 630, temperature optimization in row 631, variouspower production and consumption facilities in rows 632 through 636,being respectively solar, battery, gas generation, diesel generation,and fixed load (fixed power consumption or fixed demand).

Row 637 shows gas generation cost for the customer, and row 638 showsdiesel generation costs for the customer. Line 639 shows the retailnight cost of electricity from the customer's supplier, and line 640shows the retail day cost of electricity from the supplier. Line 641shows the generation and transmission costs reflected in retail rates.

Line 642 shows the megawatt hours of imported electricity from the gridto the facility under different optimization scenarios. Line 643 showsthe supply cost savings. Line 644 shows the demand response (reduceddemand) revenue, i.e. the revenue paid to the facility operator by theRTO for the facility generator's reduction in the facility's energyusage below the CBL. Line 645 shows the fuel costs applicable and line646 shows the net savings for the cases illustrated in the optimizationexamples.

Column 622 shows various units and prices for the respective items incolumn 621. MW abbreviates megawatts. MWh abbreviates megawatt hours.

Line 630 through 636, in column 622, shows the production capacity ofthe respective facilities. Lines 637 through 641 of column 622 shows theprices of the various factors named in column 621.

The checkmarks in lines 631 through 636 in cases 0 through 3 in columns623 through 626 indicate what options are active in the indicatedoptimization case. Lines 637 through 646 in columns 623 through 626 showthe various indicated prices and costs of the various features andoptions selected in the various cases. Line 646 shows the financialbenefit of each option.

For example, in column 626 in optimization case 3 produced by examples,temperature is optimized, and all five of the energy resources includinga solar, battery, gas generation, diesel generation and fixed load areimplicated. The applicable prices are indicated in lines 637 through641. The result in 642 is importing 63.64 megawatt hours of electricityfrom the grid (rather than the 226.64 MWH in Case 0), with a supplysavings of $9,893.02 in line 643, with demand reduction reimbursementfrom the grid to the facility in line 644 of $21,376.18, with a fuelcost to the facility in line 645 of $12,092.02, for a net savings to thecustomer in case 3 of $19,177.18 shown in line 646. Of the four casesshown in this FIG. 19, the highest net savings in line 646 is with case3, which is thereby indicated as the most optimizing case.

FIG. 20 shows a system architecture for examples that support andimplement the modules shown in FIG. 18 to produce the optimizationexample shown in FIG. 19. Appropriate computer and communicationshardware and software is used in an integration layer 704 to permitintegrated communication between the portal 509, generation forecastmodule 504, the VP (VPower) load forecast CBL 505 (the load forecast ofthe “customer base load”), the power analytics module 507, theoptimizing module 506, the model builder 502, the market interface 524,the gateway 526, the settlement module 528, the forecast data feeds 510,512 from the external services 510, 512, and the carbon footprintcalculator 508. (The same element numbers are used in FIG. 20 and FIG.18, where the same elements are referred to in both Figures.)

Furthermore, the integration layer 704 allows integrated communicationbetween these components and the PJM CBL calculator 702, the userinterface engine 706, the displays 708, and the SCADA, EMS, BMS, 540.CBL abbreviates “customer base load” for electric power and is discussedfurther herein. The PJM CBL calculator 702 is a CBL calculator providedby a specific RTO in the Northeast, that being PJM.

The VP load forecast CBL 505 is referred to in FIG. 18 as the loadforecast module 505. This is an alternative forecast of the CBL by anexample of the present disclosure. The PJM CBL calculator 702 may beused initially to forecast the CBL. However, it may be that thealternative VP load forecast CBL 505 provides a superior algorithm andmay eventually replace use of the PJM CBL calculator 702 to forecast theCBL. The system as indicated in FIG. 20 may use either or bothalternative CBL calculations 505, 702, to support the settlement module528.

The portal 509 is used by an engineer of 509 as indicated in FIG. 21 toaccess the example.

The UI engine 706 may develop, project and support the user interfaces708 used by the engineer 509, the dispatcher 530, the facility manager542, and by the market operator utility 534. The UI engine 706 projectsthe displays 708 used by the various users.

FIG. 21 is a chart describing the operation of one possible optimizationoption that may be calculated by system modules of FIG. 18 through theoptimization examples in case 3 in FIG. 19 shown in column 626, usingthe system architecture of FIG. 20.

The horizontal axis shows time over a 24-hour cycle in 30-minuteintervals. The vertical axis on the left-hand scale shows megawatts, thevertical axis on the right-hand scale shows cost in dollars. Thedifferent vertical bars show the production of electricity by a facilityin option 3 at various times during the day, produced by dieselgeneration 810, gas generation 820, solar generation 830, power batterydischarge 840, imported electricity from the RTO power grid 850, and thelocational marginal price (LMP) throughout the day is shown in the line860. Hence, we can see that under this optimization scenario, forexample electricity imported from the grid 850 is maximized during thehours around 3:30 a.m. when the LMP is the lowest, and the electricityimported from the grid 850 is reduced to zero during the hours around15:00 hours when the LMP is highest.

Also, it appears that the facility may be pre-cooled during the timearound 3:30 hours when the LMP is lowest, by a substantial use ofimported electricity.

Also, is appears that total use of electricity is peaked again in thehours around 15:00 hours when the demand for cooling is highest in theafternoon. But at this time, imported power 850 is reduced to zerobecause the LMP 860 is most expensive. This is accomplished by usingdiesel generation 810, gas generation 820, solar generation 830 (whichis possible because the sun is out), and discharging the batteries 840.The batteries have been charged during the night around 3:30 hours whenthe LMP is lowest, to be discharged in the afternoon when the LMP ishighest.

CONCLUSION

While various inventive embodiments have been described and illustratedherein, those of ordinary skill in the art will readily envision avariety of other means and/or structures for performing the functionand/or obtaining the results and/or one or more of the advantagesdescribed herein, and each of such variations and/or modifications isdeemed to be within the scope of the inventive embodiments describedherein. More generally, those skilled in the art will readily appreciatethat all parameters, dimensions, materials, and configurations describedherein are meant to be exemplary and that the actual parameters,dimensions, materials, and/or configurations will depend upon thespecific application or applications for which the inventive teachingsis/are used. Those skilled in the art will recognize, or be able toascertain using no more than routine experimentation, many equivalentsto the specific inventive embodiments described herein. It is,therefore, to be understood that the foregoing embodiments are presentedby way of example only and that, within the scope of the appended claimsand equivalents thereto, inventive embodiments may be practicedotherwise than as specifically described and claimed. Inventiveembodiments of the present disclosure are directed to each individualfeature, system, article, material, kit, and/or method described herein.In addition, any combination of two or more such features, systems,articles, materials, kits, and/or methods, if such features, systems,articles, materials, kits, and/or methods are not mutually inconsistent,is included within the inventive scope of the present disclosure.

The above-described embodiments of the invention can be implemented inany of numerous ways. For example, some embodiments may be implementedusing hardware, software or a combination thereof. When any aspect of anembodiment is implemented at least in part in software, the softwarecode can be executed on any suitable processor or collection ofprocessors, whether provided in a single computer or distributed amongmultiple computers.

In this respect, various aspects of the invention may be embodied atleast in part as a computer readable storage medium (or multiplecomputer readable storage media) (e.g., a computer memory, one or morefloppy disks, compact disks, optical disks, magnetic tapes, flashmemories, circuit configurations in Field Programmable Gate Arrays orother semiconductor devices, or other tangible computer storage mediumor non-transitory medium) encoded with one or more programs that, whenexecuted on one or more computers or other processors, perform methodsthat implement the various embodiments of the technology discussedabove. The computer readable medium or media can be transportable, suchthat the program or programs stored thereon can be loaded onto one ormore different computers or other processors to implement variousaspects of the present technology as discussed above.

The terms “program” or “software” are used herein in a generic sense torefer to any type of computer code or set of computer-executableinstructions that can be employed to program a computer or otherprocessor to implement various aspects of the present technology asdiscussed above. Additionally, it should be appreciated that accordingto one aspect of this embodiment, one or more computer programs thatwhen executed perform methods of the present technology need not resideon a single computer or processor, but may be distributed in a modularfashion amongst a number of different computers or processors toimplement various aspects of the present technology.

Computer-executable instructions may be in many forms, such as programmodules, executed by one or more computers or other devices. Generally,program modules include routines, programs, objects, components, datastructures, etc. that perform particular tasks or implement particularabstract data types. Typically the functionality of the program modulesmay be combined or distributed as desired in various embodiments.

Also, the technology described herein may be embodied as a method, ofwhich at least one example has been provided. The acts performed as partof the method may be ordered in any suitable way. Accordingly,embodiments may be constructed in which acts are performed in an orderdifferent than illustrated, which may include performing some actssimultaneously, even though shown as sequential acts in illustrativeembodiments.

All definitions, as defined and used herein, should be understood tocontrol over dictionary definitions, definitions in documentsincorporated by reference, and/or ordinary meanings of the definedterms.

The indefinite articles “a” and “an,” as used herein in thespecification and in the claims, unless clearly indicated to thecontrary, should be understood to mean “at least one.”

The phrase “and/or,” as used herein in the specification and in theclaims, should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases. Multiple elements listed with“and/or” should be construed in the same fashion, i.e., “one or more” ofthe elements so conjoined. Other elements may optionally be presentother than the elements specifically identified by the “and/or” clause,whether related or unrelated to those elements specifically identified.Thus, as a non-limiting example, a reference to “A and/or B”, when usedin conjunction with open-ended language such as “comprising” can refer,in one embodiment, to A only (optionally including elements other thanB); in another embodiment, to B only (optionally including elementsother than A); in yet another embodiment, to both A and B (optionallyincluding other elements); etc.

As used herein in the specification and in the claims, “or” should beunderstood to have the same meaning as “and/or” as defined above. Forexample, when separating items in a list, “or” or “and/or” shall beinterpreted as being inclusive, i.e., the inclusion of at least one, butalso including more than one, of a number or list of elements, and,optionally, additional unlisted items. Only terms clearly indicated tothe contrary, such as “only one of” or “exactly one of,” or, when usedin the claims, “consisting of,” will refer to the inclusion of exactlyone element of a number or list of elements. In general, the term “or”as used herein shall only be interpreted as indicating exclusivealternatives (i.e. “one or the other but not both”) when preceded byterms of exclusivity, such as “either,” “one of,” “only one of,” or“exactly one of.” “Consisting essentially of,” when used in the claims,shall have its ordinary meaning as used in the field of patent law.

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified. Thus, as anon-limiting example, “at least one of A and B” (or, equivalently, “atleast one of A or B,” or, equivalently “at least one of A and/or B”) canrefer, in one embodiment, to at least one, optionally including morethan one, A, with no B present (and optionally including elements otherthan B); in another embodiment, to at least one, optionally includingmore than one, B, with no A present (and optionally including elementsother than A); in yet another embodiment, to at least one, optionallyincluding more than one, A, and at least one, optionally including morethan one, B (and optionally including other elements); etc.

In the claims, as well as in the specification above, all transitionalphrases such as “comprising,” “including,” “carrying,” “having,”“containing,” “involving,” “holding,” “composed of,” and the like are tobe understood to be open-ended, i.e., to mean including but not limitedto. Only the transitional phrases “consisting of” and “consistingessentially of” shall be closed or semi-closed transitional phrases,respectively, as set forth in the United States Patent Office Manual ofPatent Examining Procedures, Section 2111.03.

What is claimed is:
 1. An apparatus for determining an operatingschedule of a controller of at least one energy storage asset operatedby an energy customer of an electricity supplier, so as to generateenergy-related revenue, over a time period T, associated with operationof the at least one energy storage asset according to the operatingschedule, wherein the energy-related revenue available to the energycustomer over the time period T is based at least in part on a wholesaleelectricity market, the apparatus comprising: at least one communicationinterface; at least one memory to store processor-executableinstructions and a mathematical model for the at least one energystorage asset, wherein the mathematical model facilitates adetermination of the operating schedule for the controller of the atleast one energy storage asset based at least in part on a firstoperation characteristic of the at least one energy storage asset, asecond operation characteristic of at least one energy consuming assetin communication with the at least one energy storage asset, and aforecast wholesale electricity price associated with the wholesaleelectricity market; and at least one processing unit, communicativelycoupled to the at least one communication interface and the at least onememory, wherein upon execution of the processor-executable instructions,the at least one processing unit: A) determines the operating schedulefor the controller of the at least one energy storage asset using themathematical model, wherein the operating schedule for the controller ofthe at least one energy storage asset specifies, during a time intervalless than time period T, a proportion of an available state of charge(SOC) of the energy storage asset for use in an energy market and aremaining proportion of the available SOC of the energy storage assetfor use in a regulation market; and B) controls the at least onecommunication interface to transmit to the energy customer the operatingschedule for the controller of the at least one energy storage assetdetermined in A), and/or controls the at least one memory so as to storethe determined operating schedule for the controller.
 2. The apparatusof claim 1, wherein the first operation characteristic of the at leastone energy storage asset is at least one of a state of charge, a chargerate, a degree of non-linearity of charge rate a discharge rate, adegree of non-linearity of discharge rate, a round trip efficiency, anda degree of life reduction.
 3. The apparatus of claim 2, wherein theproportion of the available SOC of the at least one energy storage assetfor use in the energy market is supplied as a direct-current (DC)signal, and wherein the remaining proportion of the available SOC of theat least one energy storage asset for use in the regulation market isdelivered at a variable charge rate or variable discharge rate.
 4. Theapparatus of claim 1, wherein a sum of the proportion of the availableSOC of the at least one energy storage asset for use in the energymarket and the remaining proportion of the available SOC of the at leastone energy storage asset for use in the regulation market is greaterthan a minimal allowed SOC of the at least one energy storage asset andless than a maximal allowed SOC of the at least one energy storageasset.
 5. The apparatus of claim 1, wherein, upon execution of theprocessor-executable instructions, the at least one processing unitdetermines the operating schedule for the controller of the at least oneenergy storage asset using the mathematical model in A) by minimizing anet energy-related cost over the time period T, wherein: the net-energyrelated cost is based at least in part on: electricity generation by theat least one energy storage asset, first electricity consumption by theat least one energy storage asset, and second electricity consumption bythe at least one energy consuming asset; and the energy-related revenueavailable to the energy customer is based at least in part on theminimized net energy-related cost.
 6. The apparatus of claim 5, whereinthe net energy-related cost is specified as a difference between anelectricity supply cost and an economic demand response revenue over thetime period T.
 7. The apparatus of claim 6, wherein in A), the at leastone processing unit: determines the operating schedule for thecontroller of the at least one energy storage asset using themathematical model and a representative customer baseline (CBL) energyprofile for the at least one energy consuming asset, over the timeperiod T, wherein the representative CBL energy profile represents atypical operation of the at least one energy consuming asset by theenergy customer.
 8. The apparatus of claim 7, wherein the representativeCBL is an energy consumption profile as a function of time for the atleast one energy consuming asset.
 9. The apparatus of claim 7, whereinthe economic demand response revenue over the time period T isdetermined based on, the forecast wholesale electricity price, theelectricity generation by the at least one energy storage asset for usein the energy market, a regulation price, and a time period that the atleast one energy storage asset is used in the regulation market.
 10. Theapparatus of claim 6, wherein: the at least one energy consuming assetincludes at least one controllable energy consuming asset; the operatingschedule for the controller of the at least one energy storage assetconstitutes a first operating schedule; and in A), the at least oneprocessing unit determines both the first operating schedule for thecontroller of the at least one energy storage asset and a secondoperating schedule for the at least one controllable energy consumingasset, based at least in part on minimizing the net energy-related cost,over the time period T, associated with the electricity generation bythe at least one energy storage asset, the first electricity consumptionby the at least one energy storage asset, and the second electricityconsumption by the at least one controllable energy consuming asset. 11.The apparatus of claim 10, wherein in A), the at least one processingunit: determines the first operating schedule for the controller of theat least one energy storage asset and the second operating schedule forthe at least one controllable energy consuming asset using themathematical model and a representative customer baseline (CBL) energyprofile for the at least one controllable energy consuming asset, overthe time period T, wherein the representative CBL energy profilerepresents a typical operation of the at least one controllable energyconsuming asset by the energy customer as specified by abusiness-as-usual (BAU) operating schedule for the at least onecontrollable energy consuming asset.
 12. The apparatus of claim 11,wherein the economic demand response revenue over the time period T isdetermined based on the forecast wholesale electricity price, theelectricity generation by the at least one energy storage asset, thefirst electricity consumption by the at least one energy storage asset,and a difference between the second electricity consumption by the atleast one controllable energy consuming asset and the representative CBLenergy profile for the at least one controllable energy consuming asset.13. The apparatus of claim 12, wherein in A), the at least oneprocessing unit: A1) selects a plurality of first candidate operatingschedules for the controller of the at least one energy storage asset,and selects a plurality of second candidate operating schedules for theat least one controllable energy consuming asset, wherein each secondcandidate operating schedule is different from the BAU operatingschedule for the at least one controllable energy consuming asset; A2)successively applies the plurality of first candidate operatingschedules and the plurality of second candidate operating schedules tothe mathematical model to generate a corresponding plurality ofsimulated energy profiles for the at least one energy storage asset andthe at least one controllable energy consuming asset; A3) calculates aplurality of projected net energy-related costs to the energy customer,wherein each projected net energy-related cost is computed based atleast in part on the representative CBL energy profile and the simulatedenergy profiles corresponding to the respective first and secondcandidate operating schedules, and the forecast wholesale electricityprice; and A4) selects, as an optimal first operating schedule and anoptimal second operating schedule, respective ones of the first andsecond candidate operating schedules corresponding to one simulatedenergy profile of the plurality of simulated energy profiles thatresults in a minimum net energy-related cost of the plurality of netenergy-related costs calculated in A3).
 14. The apparatus of claim 12,wherein in B) the at least one processing unit: controls the at leastone communication interface to transmit to the energy customer the firstoperating schedule for the controller of the at least one energy storageasset and the second operating schedule for the at least onecontrollable energy consuming asset determined in A), and/or controlsthe at least one memory so as to store the determined first operatingschedule for the controller and the second operating schedule for the atleast one controllable energy consuming asset.
 15. The apparatus ofclaim 12, wherein: the at least one controllable energy consuming assetincludes at least one building having a variable internal temperaturecontrolled by a heating, ventilation and air conditioning (HVAC) system;the second operating schedule for the at least one controllable energyconsuming asset specifies a candidate temperature set point for the HVACsystem as a function of time; and the BAU operating schedule for the atleast one controllable energy consuming asset is specified by abusiness-as-usual (BAU) temperature set point for the HVAC system as afunction of time.
 16. The apparatus of claim 12, wherein in A), the atleast one processing unit: determines the first operating schedule forthe controller of the at least one energy storage asset and the secondoperating schedule for the at least one controllable energy consumingasset using the mathematical model and a comfort cost attributed to achange in the energy customer's behavior in adopting the secondoperating schedule for the at least one controllable energy consumingasset instead of the BAU operating schedule.
 17. The apparatus of claim16, wherein the comfort cost is specified as a cost function based atleast in part on at least one difference between the second operatingschedule for the at least one controllable energy consuming asset andthe BAU operating schedule.
 18. The apparatus of claim 1, wherein theoperating schedule for the controller of the at least one energy storageasset specifies a time interval within the time period T for use of alarger proportion of the available SOC of the at least one energystorage asset to power the energy consuming asset when the forecastwholesale electricity price exceeds a predetermined threshold value. 19.The apparatus of claim 1, wherein the operating schedule for thecontroller of the at least one energy storage asset specifies during atime interval within the time period T for use of a larger proportion ofthe available SOC of the at least one energy storage asset in theregulation market when the forecast wholesale price is below apredetermined threshold value.
 20. The apparatus of claim 1, wherein themathematical model facilitates determination of the operating schedulefor the controller of the at least one energy storage asset furtherbased at least in part on an expected energy-generating schedule of anenergy generating asset in communication with the energy storage assetand the energy consuming asset.
 21. The apparatus of claim 20, whereinthe energy generating asset is at least one photovoltaic cell, at leastone fuel cell, at least one gas turbine, at least one diesel generator,at least one flywheel, at least one electric vehicle, or at least onewind turbine.
 22. The apparatus of claim 1, wherein the energy storageasset is at least one battery, at least one ice unit, or compressed air.23. The apparatus of claim 22, wherein the energy storage asset is atleast one battery, and wherein the at least one battery is lithium ionbattery, lead acid battery, a flow battery, or a dry cell battery. 24.The apparatus of claim 1, wherein the controller facilitates thecommunication between the at least one energy consuming asset and the atleast one energy storage asset.
 25. The apparatus of claim 1, whereinthe first operation characteristic of the at least one energy storageasset is at least one of a state of charge, a charge rate, a degree ofnon-linearity of charge rate a discharge rate, a degree of non-linearityof discharge rate, a round trip efficiency, and a degree of lifereduction.
 26. The apparatus of claim 1, wherein the second operationcharacteristic of the at least one energy consuming asset is a load useschedule of the at least one energy consuming asset.
 27. The apparatusof claim 26, wherein the second operation characteristic of the at leastone energy consuming asset is an energy consumption profile as afunction of time of the at least one energy consuming asset.
 28. Theapparatus of claim 26, wherein the at least one energy consuming assetis a controllable energy consuming asset, and wherein the secondoperation characteristic of the at least one controllable energyconsuming asset is a set point.
 29. An apparatus for determining anoperating schedule of a controller of at least one energy storage assetoperated by an energy customer of an electricity supplier, so as togenerate energy-related revenue, over a time period T, associated withoperation of the at least one energy storage asset according to theoperating schedule, wherein the energy-related revenue available to theenergy customer over the time period T is based at least in part on awholesale electricity market, and wherein the wholesale electricitymarket includes an energy market and a regulation market, the apparatuscomprising: at least one communication interface; at least one memory tostore processor-executable instructions and a mathematical model for theat least one energy storage asset, wherein the mathematical modelfacilitates a determination of the operating schedule for the controllerof the at least one energy storage asset based at least in part on anoperation characteristic of the at least one energy storage asset, aforecast wholesale electricity price associated with the energy market,and a regulation price associated with the regulation market; and atleast one processing unit, communicatively coupled to the at least onecommunication interface and the at least one memory, wherein uponexecution of the processor-executable instructions, the at least oneprocessing unit: A) determines the operating schedule for the controllerof the at least one energy storage asset using the mathematical model byminimizing a net energy-related cost over the time period T, wherein:the net-energy related cost is based at least in part on: duration ofenergy storage asset participation in the regulation market; electricitygeneration by the at least one energy storage asset; and electricityconsumption by the at least one energy storage asset; and theenergy-related revenue available to the energy customer is based atleast in part on the minimized net energy-related cost; and wherein theoperating schedule specifies, during a time interval within the timeperiod T, a first portion of an available output of the controller foruse in the energy market and a second portion of the available output ofthe controller for use for use in the regulation market; and B) controlsthe at least one communication interface to transmit to the energycustomer the operating schedule for the controller of the at least oneenergy storage asset determined in A), and/or controls the at least onememory so as to store the determined operating schedule for thecontroller.
 30. The apparatus of claim 29, wherein the available outputof the controller is a charge rate of the at least one energy storageasset or a discharge rate of the at least one energy storage asset. 31.The apparatus of claim 29, wherein the net energy-related cost isspecified as a difference between an electricity supply cost and aneconomic demand response revenue over the time period T.
 32. Theapparatus of claim 29, wherein the operation characteristic of the atleast one energy storage asset is at least one of a state of charge, acharge rate, a degree of non-linearity of charge rate a discharge rate,a degree of non-linearity of discharge rate, a round trip efficiency,and a degree of life reduction.
 33. An apparatus for determining anoperating schedule of a controller of at least one energy storage assetoperated by an energy customer of an electricity supplier, so as togenerate energy-related revenue, over a time period T, associated withoperation of the at least one energy storage asset according to theoperating schedule, wherein the energy-related revenue available to theenergy customer over the time period T is based at least in part on awholesale electricity market, and wherein the wholesale electricitymarket includes an energy market and a regulation market; the apparatuscomprising: at least one communication interface; at least one memory tostore processor-executable instructions and a mathematical model for theat least one energy storage asset, wherein the mathematical modelfacilitates a determination of the operating schedule for the controllerof the at least one energy storage asset based at least in part on anoperation characteristic of the at least one energy storage asset, anexpected energy-generating schedule of an energy generating asset incommunication with the energy storage asset, a forecast wholesaleelectricity price associated with the energy market, and a regulationprice associated with the regulation market; and at least one processingunit, communicatively coupled to the at least one communicationinterface and the at least one memory, wherein upon execution of theprocessor-executable instructions, the at least one processing unit: A)determines the operating schedule for the controller of the at least oneenergy storage asset using the mathematical model by minimizing a netenergy-related cost over the time period T, wherein: the net-energyrelated cost is based at least in part on: amount of energy generationby the at least one energy generating asset; duration of energy storageasset participation in the regulation market; electricity generation bythe at least one energy storage asset; and electricity consumption bythe at least one energy storage asset; and the energy-related revenueavailable to the energy customer is based at least in part on theminimized net energy-related cost; and wherein the operating schedulespecifies, during a time interval within the time period T, a firstportion of an available output of the controller for use in the energymarket and a second portion of the available output of the controllerfor use for use in the regulation market; and B) controls the at leastone communication interface to transmit to the energy customer theoperating schedule for the controller of the at least one energy storageasset determined in A), and/or controls the at least one memory so as tostore the determined operating schedule for the controller.
 34. Theapparatus of claim 33, wherein the available output of the controller isa charge rate of the at least one energy storage asset or a dischargerate of the at least one energy storage asset.
 35. The apparatus ofclaim 33, wherein the net energy-related cost is specified as adifference between an electricity supply cost and an economic demandresponse revenue over the time period T.
 36. The apparatus of claim 33,wherein the operation characteristic of the at least one energy storageasset is at least one of a state of charge, a charge rate, a degree ofnon-linearity of charge rate a discharge rate, a degree of non-linearityof discharge rate, a round trip efficiency, and a degree of lifereduction.